Archives of: New York Logic Seminars

MAMLS Logic Friday, New York, October 27, 2017

Mid-Atlantic Mathematical Logic Seminar

CUNY Graduate Center

October 27, 2017

Room 6417

MAMLS Logic Friday is a one-day logic meeting taking place at the CUNY Graduate Center with the support of the National Science Foundation. It will feature talks in set theory, computability theory, and model theory.

While graduate students, young researchers, female mathematicians and members of underrepresented groups are particularly encouraged to apply for travel support, it should be stressed that any participants without their own sources of funding are eligible to apply. Requests will be handled on a case-by-case basis within the limits of the budget. To apply for travel support or to find out more information, please contact Victoria Gitman (vgitman@nylogic.org).

Information about hotels can be found here.

Speakers

Schedule

9:00-9:30
Breakfast (Math Lounge 4214)

Morning Session

9:30-10:15
Ivo Herzog
The Logic of Positive Primitive Formulae
We will discuss the structure of positive primitive formulae in the language of modules over a ring R. This structure includes two cubical lattices related by the Prest dual. We place particular emphasis on the resemblance of positive primitive logic to quantum logic and von Neumann’s work on the coordinatization of complemented modular lattices. For a ring (R,*) with involution, this gives rise to a quantum logic coordinatized by a *-regular ring obtained by adjusting a classical construction of Olivier for commutative rings.

10:30-11:15
Tim McNicholl
Computable metric structure theory
I will begin by reviewing the evolution of computable structure theory beginning with its origins in the work of van der Waerden on constructive algebra. I will then discuss recent work on extending the computable structures program to metric structures by means of the framework of computable analysis. I will focus on Banach spaces, and in particular recent results on computable categoricity and degrees of categoricity of

spaces. The solutions of some of the resulting problems involve am interesting blend of methods from functional analysis and classical computability theory.

Lunch

11:30-12:30
Lunch Break

Afternoon Session

12:45-1:30
Chris Lambie-Hanson
Reflections on graph coloring
In 1951, de Bruijn and Erdős published a compactness theorem for graphs with finite chromatic number, proving that, if is a graph, is a natural number, and all finite subgraphs of have chromatic number at most , then has chromatic number at most . Since then, infinitary generalizations of this theorem, for the chromatic number as well as the coloring number of graphs, have attracted much attention. In this talk, we will briefly review some of the historical highlights in this area and then present some new work. These results show that the coloring number can exhibit only a limited amount of incompactness, while large amounts of incompactness for the chromatic number are implied by relatively weak hypotheses. This indicates that the coloring number and chromatic number behave quite differently with respect tocompactness and illustrates the difficulty involved in obtaining infinitary analogues of the de Bruijn-Erdős result at infinite, accessible cardinals. This is joint work with Assaf Rinot.

1:45-2:30
Matthew Harrison-Trainor
Some Computable Structure Theory of Finitely Generated Structures
Every countable structure has a sentence of infinitary logic, called a Scott sentence, which describes it up to isomorphism among countable structures. We can characterize the complexity of a structure by the complexity of the simplest description of that structure. A finitely generated structure always has a

description. We show that there is a finitely generated group which has no simpler description. The proof of this leads us to talk about notions of universality for finitely generated structures. Finitely generated groups are universal, but finitely generated fields are not. By this, we mean that for every finitely generated structure, there is a finitely generated group which has the same computability-theoretic properties; but the same is not true for finitely generated fields. We apply the results of this investigation to pseudo Scott sentences.

2:45-3:30
Stamatis Dimopoulos
Woodin-for-strong-compactness cardinals, a new identity crisis
Woodin and Vopěnka cardinals are established notions in the large cardinal hierarchy and despite being defined in different context, they proved to be very similar. In fact, Vopěnka cardinals are obtained by replacing a strongness clause in the definition of Woodinness by a supercompactness clause. Since strong compactness is an intermediate large cardinal notion between strongness and supercompactness, it is natural to consider a “Woodinised” version of it. In this talk, we give the definition of this new type of large cardinal, called Woodin for strong compactness, and will present some results about them. The highlight is that the analogue of Magidor’s “identity crisis” theorem for the first strongly compact holds for these cardinals too: the first Woodin for strong compactness cardinal can consistently be the first Woodin or the first Vopěnka cardinal.

This Week in Logic at CUNY

Computational Logic Seminar
Tuesday, November 26, 2013 2:00 pm Graduate Center, rm. 3209 
Speaker: Che-Ping Su The University of Melbourne
Title: Paraconsistent Justification Logic
Link: http://nylogic.org/talks/paraconsistent-justification-logic 

In the literature of belief revision, there is one approach called belief base belief revision, where the belief set is not required to be closed under a consequence relation. According to Sven Ove Hansson, in belief base belief revision, there are two ways to define the revision operator:
revision = expansion + contraction
revision = contraction + expansion
Hansson has a result that these two ways of defining the revision operator do not collapse into the same operator. Hansson also thinks that in the first way, there is an intermediate inconsistent epistemic state that occurs after expansion. Paraconsistent justification logic is intended to model the agent’s justification structure, when the agent is in such an inconsistent epi-state. My hope is that this logic could help us better model belief revision.

In my talk, the motivation will be better clarified. And, a paraconsistent justification logic system will be introduced.

Model theory seminar
Friday, December 6, 2013 12:30 pm GC 6417 
Speaker: Manuel Alves CUNY Grad Center
Title: TBA
Link: http://nylogic.org/talks/tba-8

This Week in Logic at CUNY

Computational Logic Seminar

Tuesday, November 19, 2013 2:00 pm Graduate Center, rm. 3209 
Speaker: Vincent Fella Hendricks University of Copenhagen
Title: Structures of Social Proof
Link: http://nylogic.org/talks/structures-of-social-proof 

“Social proof” means that single agents assume beliefs, norms or actions of other agents in an attempt to reflect the correct view, stance, behavior for a given situation. The structure and modularity of social proof is unravelled including formal characterizations of derived socio-informational phenomena like bystander-effects and cascades. Sometimes social proof may be responsible for information spinning out of control – in very unfortunate ways. Joint work with Rasmus K. Rendsvig.

Models of PA

Wednesday, November 20, 2013 6:30 pm GC 4214.03 
Speaker: Athar Abdul-Quader CUNY Grad Center
Title: When are subsets of a model “coded”?
Link: http://nylogic.org/talks/when-are-subsets-of-a-model-coded 

I will present a result by J. Schmerl that characterizes when a collection of subsets of a given model, M, will appear as the coded sets in some elementary end extension of M. This is an analogue to Scott’s theorem, which characterizes when a collection of sets of natural numbers can be the standard system of some model of PA. If there is time, I will also present some extensions of the result.

HoTT Reading Group

Thursday, November 21, 2013 7:00 am Graduate Center, Room 6417 
Speaker: Dustin Mulcahey
Title: Types, Spaces, and Higher Groupoids
Link: http://nylogic.org/talks/types-spaces-and-higher-groupoids 

Last time we discussed fibrations of sets, spaces, and types. We noted that path induction allows us to prove that the type family of equalities over a given type A is “homotopy equivalent” to A.

This week, we will continue with this and discuss the groupoid structure of spaces (paths) and types (equalities). In doing so, we will establish the “interchange law” for 2-categories, and see that in the particular case of spaces and types that this allows us to prove that the composition law is commutative (up to a higher equivalence) for 2-paths and 2-equivalences that begin and end at the same point.

We shall also discuss how non-dependent functions between types give rise to functors on the associated groupoids of equivalences. This leads to the problem of what to do for dependent functions, and it turns out that fibrations give us a solution to this, and thus we will have come full circle.

Model theory seminar

Friday, November 22, 2013 12:30 pm 
Speaker: Alice Medvedev City College — CUNY
Title: TBA
Link: http://nylogic.org/talks/tba-5 

CUNY Logic Workshop
Friday, November 22, 2013 2:00 pm GC 6417 
Speaker: Tamar Lando Columbia University
Title: Measure semantics for modal logics
Link: http://nylogic.org/talks/tamar-lando 

Long before Kripke semantics became standard in modal logic, Tarski showed us that the basic propositional modal language can be interpreted in topological spaces. In Tarski’s semantics for the modal logic $S4$, each propositional variable is evaluated to an arbitrary subset of a fixed topological space. I develop a related, measure theoretic semantics, in which modal formulas are interpreted in the Lebesgue measure algebra, or algebra of Borel subsets of the real interval $[0,1]$, modulo sets of measure zero. This semantics was introduced by Dana Scott in the last several years. I discuss some of my own completeness results, and ways of extending the semantics to more complex modal languages.

Computational Logic Seminar

Tuesday, November 26, 2013 2:00 pm Graduate Center, rm. 3209 
Speaker: Che-Ping Su The University of Melbourne
Title: Paraconsistent Justification Logic
Link: http://nylogic.org/talks/paraconsistent-justification-logic 

In the literature of belief revision, there is one approach called belief base belief revision, where the belief set is not required to be closed under a consequence relation. According to Sven Ove Hansson, in belief base belief revision, there are two ways to define the revision operator:
revision = expansion + contraction
revision = contraction + expansion
Hansson has a result that these two ways of defining the revision operator do not collapse into the same operator. Hansson also thinks that in the first way, there is an intermediate inconsistent epistemic state that occurs after expansion. Paraconsistent justification logic is intended to model the agent’s justification structure, when the agent is in such an inconsistent epi-state. My hope is that this logic could help us better model belief revision.

In my talk, the motivation will be better clarified. And, a paraconsistent justification logic system will be introduced.

This Week in Logic at CUNY

Computational Logic Seminar
Tuesday, November 12, 2013 2:00 pm Graduate Center, rm. 3209 
Speaker: Melvin Fitting Lehman College – CUNY Graduate Center
Title: Realization Semantically
Link: http://nylogic.org/talks/realization-semantically 

This talk continues my previous one from October 22. In that, I gave justification counterparts for S4.2 and for K4^3, possible world justification semantics, and a completeness proof. The completeness proof used a canonical model construction. Now I’l use that canonical model to prove, non-constructively, realization theorems for the two logics. The methodology is the same as in a paper of mine published in 2005, though the presentation has change somewhat. Primarily my motivation is to explore the range of modal logics having justification counterparts—to discover its extent and limits.

 

Models of PA
Wednesday, November 13, 2013 6:30 pm GC 4214.03 
Speaker: Alf Dolich The City University of New York
Title: How to make a full satisfaction class
Link: http://nylogic.org/talks/how-to-make-a-full-satisfaction-class 

NYCAC 6
The New York Colloquium on Algorithms and Complexity
Friday, November 15, 2013
The Graduate Center, CUNY
Room 4102 (Science Center)
NYCAC, the New York Colloquium on Algorithms and Complexity is an annual event.  Its purpose is to give the opportunity to graduate students in New York to observe talks of researchers from all areas of the theory of Algorithms and Computational Complexity.
Invited Speakers
Eric Allender (Rutgers U.)
Wen-Ju Cheng (Graduate Center, CUNY)
Constantinos Daskalakis (MIT)
Rosario Gennaro (CCNY, CUNY)
Steve Homer (Boston U.)
Valia Mitsou (GC, CUNY)
Charalampos (Babis) Papamanthou (U. Maryland)
Dimitris Paparas (Columbia U.)
Kenneth W. Regan (U. Buffalo, SUNY)
On the same day the NYC CryptoDay at NYU will take place.  Visit http://nycryptoday.wordpress.com/ for more information.
Set theory seminar
Friday, November 15, 2013 10:00 am 
Speaker: Victoria Gitman The New York City College of Technology (CityTech), CUNY
Title: A Jónsson ω1-like model of set theory
Link: http://nylogic.org/talks/a-jonsson-omega_1-like-model-of-set-theoryA first-order structure of cardinality κ is said to be Jónsson if it has no proper elementary substructure of cardinality κ. The speaker will prove a theorem of Julia Knight that there is a Jónsson ω1-like model of set theory.

Model theory seminar
Friday, November 15, 2013 12:30 pm GC 6417 
Speaker: Yevgeniy Vasilyev Memorial University of Newfoundland and Christopher Newport University
Title: On dense independent subsets of geometric structures
Link: http://nylogic.org/talks/on-dense-independent-subsets-of-geometric-structures 

We consider expansions of geometric theories obtained by adding a predicate distinguishing a “dense” independent subset, generalizing a construction introduced by A. Dolich, C. Miller and C. Steinhorn in the o-minimal context. The expansion preserves many of the properties related to stability, simplicity, rosiness and NIP. We also study the structure induced on the predicate, and show that despite its geometric triviality, it inherits most of the “combinatorial” complexity of the original theory. This is a joint work with Alexander Berenstein.

CUNY Logic Workshop
Friday, November 15, 2013 2:00 pm GC 6417 
Speaker: Alice Medvedev City College — CUNY
Title: Title TBA
Link: http://nylogic.org/talks/title-tba-6

This Week in Logic at CUNY

Computational Logic Seminar

Tuesday, November 5, 2013 2:00 pm Graduate Center, rm. 3209
Speaker: Elena Nogina The City University of New York
Title: Reflection Principles Involving Provability and Explicit Proofs
Link: http://nylogic.org/talks/reflection-principles-involving-provability-and-explicit-proofs 

Reflection principles are classical objects in proof theory and the areas studying Gödel’s Incompleteness. Reflection principles based on provability predicates were introduced in the 1930s by Rosser and Turing, and later were explored by Feferman, Kreisel & Levi, Schmerl, Artemov, Beklemishev and others.

We study reflection principles of Peano Arithmetic involving both Proof and Provability predicates. We find a classification of these principles and establish their linear ordering with respect to their metamathematical strength.

 

Models of PA
Wednesday, November 6, 2013 6:30 pm GC 4214.03
Speaker: Kerry Ojakian Bronx Community College
Title: Tanaka’s embedding theorem
Link: http://nylogic.org/talks/tanakas-embedding-theorem 

HoTT Reading Group
Thursday, November 7, 2013 7:00 am CUNY Graduate Center, Room 6417
Speaker: Dustin Mulcahey
Title: Path Induction and the Path-Loop Space Fibration
Link: http://nylogic.org/talks/path-induction-and-the-path-loop-space-fibration 

As we continue our foray into the book, we begin to view types as spaces (or, “equivalently”, as omega groupoids). My goal for this section is to focus on the path induction rule and argue that it corresponds to the path-loop fibration.

More specifically, we can make an analogy between the path space over a space X and the type of all equivalences over a type A. The path space of X is homotopy equivalent to X, and I argue that path induction says “essentially the same thing” about the type of all equivalences over A. I aim to make this analogy as formal as possible, and then delve further into the material in chapter 2.

I would also like to go over some exercises. I’ve done a few, but if anyone wants to come up to the board and show off, then they are welcome!
 

Set theory seminar
Friday, November 8, 2013 10:00 am
Speaker: Miha Habič The CUNY Graduate Center
Title: Grounded Martin’s axiom
Link: http://nylogic.org/talks/grounded-martins-axiom 

I will present a weakening of Martin’s axiom which asserts the existence of partial generics only for ccc posets contained in a ccc ground model. This principle, named the grounded Martin’s axiom, emerges naturally in the analysis of the Solovay-Tennenbaum proof of the consistency of MA. While the grounded MA has some of the combinatorial consequences of MA, it will be shown to be more flexible (being consistent with a singular continuum, for example) and more robust under forcing (being preserved in a strong way under both adding a Cohen or a random real).

Model theory seminar
Friday, November 8, 2013 12:30 pm GC6417
Speaker: Chris Miller Ohio State University
Title: A class of strange expansions of dense linear orders by open sets
Link: http://nylogic.org/talks/a-class-of-strange-expansions-of-dense-linear-orders-by-open-sets 

There are expansions of dense linear orders by open sets (of arbitrary arities) such that all of the following hold:

1) Every definable set is a boolean combination of existentially definable sets.
2) Some definable sets are not existentially definable.
3) Some projections of closed bounded definable sets are somewhere both dense and codense.
4) There is a unique maximal reduct having the property that every unary definable set either has interior or is nowhere dense. It properly expands the underlying order, yet is still rather trivial.

At least some of these structures come up naturally in model theory. For example, if G is a generic predicate for the real field, then the expansion of (G,<) by the G-traces of all semialgebraic open sets is such a structure, which moreover is interdefinable with the structure induced on G in (R,+,x,G).

CUNY Logic Workshop
Friday, November 8, 2013 2:00 pm GC 6417
Speaker: Gunter Fuchs The City University of New York
Title: Prikry-type sequences, iterations and critical sequences
Link: http://nylogic.org/talks/gunter-fuchs 

I will present some old, some new and some classic results on the kinds of sequences which are added by some forcings which are related to Prikry forcing, in some sense. After finding combinatorial properties characterizing these sequences, I will show how to iterate the universe in such a way that the critical sequence of that iteration will satisfy that combinatorial property with respect to the target model, rendering it generic. This connection enables us to analyze precisely the collection of generic sequences which are present in one specific forcing extension. Time permitting, I will also explore connections to Boolean ultrapowers.

This Week in Logic at CUNY

NOTE: the Seminar in Logic and Games meeting this Friday will be in room 4419.

Models of PA
Wednesday, October 30, 2013 6:30 pm GC 4214.03

Speaker: Erez Shochat St. Francis College
Title: Schmerl’s Lemma and Boundedly Saturated Models II
Link: http://nylogic.org/talks/schmerls-lemma-and-boundedly-saturated-models-ii 

Set theory seminar
Friday, November 1, 2013 10:00 am GC 6417
Speaker: Karel Hrbacek City College of New York, CUNY
Title: Some problems motivated by nonstandard set theory
Link: http://nylogic.org/talks/some-problems-motivated-by-nonstandard-set-theoryNonstandard set theory enriches the usual set theory by a unary “standardness” predicate.  Investigations of its foundations raise a number of questions that can be formulated in ZFC or GB and appear open.  I will discuss several such problems concerning elementary embeddings, ultraproducts, ultrafilters and large cardinals.

Model theory seminar
Friday, November 1, 2013 12:30 pm GC6417
Speaker: David Lippel Haverford College
Title: Reverse VC calculations
Link: http://nylogic.org/talks/tba-6Let F be a family of sets, for example, a uniformly definable semi-algebraic family in real or p-adic n-space. The Vapnik-Chervonenkis (VC) dimension of F is a measurement of the combinatorial complexity of F. Once you know the VC dimension of F, theorems from computational geometry, like the Epsilon-Net Theorem, give nice geometric consequences for F. I will discuss a statistical strategy for reversing the flow of information in this theorem. Instead of starting with knowledge of the VC dimension, we merely hypothesize “dimension=d” for some value d. Then, we observe the geometric behavior of F using computer experiments and compare the observed behavior with the behavior that is predicted by the theorem (under the hypothesis “dimension=d”). If our observed results have sufficiently low probability (conditioned on “dimension=d”), then we can reject the hypothesis “dimension=d” with a high degree of confidence. Ultimately, we hope to use such methods to shed light on conjectures about VC density in the p-adics. This project is joint work with Deirdre Haskell and Nigel Pynn-Coates.

CUNY Logic Workshop
Friday, November 1, 2013 2:00 pm GC 6417
Speaker: Cameron Donnay Hill Department of Mathematics and Computer Science, Wesleyan University
Title: Category, Measure, and Expansions of Countably Categorical Structures
Link: http://nylogic.org/talks/cameron-hillA natural way to approach expansions of a fixed countably-categorical structure is through the compact metric space such expansions. In this talk, I will discuss some ways to recover “typical” but constrained expansions of a fixed structure from the points of view of measure and category. Regarding measure, I will discuss a slight generalization, and a new proof, of a result of Ackerman-Freer-Patel on concentrating invariant measures on the isomorphism type of a structure. And for category, I will discuss using certain kinds of ultrafilters to extract a “generic profile” of a given expansion. Time permitting, I will share some applications to zero-one laws, structural Ramsey theory, and/or regularity properties of definable graphs in finite fields.

 
Seminar in Logic and Games
Friday, November 1, 2013, 4:15 PM room 4410
Speaker: Eric Pacuit (University of Maryland)
Title: Dynamic Logics of Evidence Based Beliefs
 
Abstract:   The intuitive notion of evidence has both semantic and syntactic features. In this talk, I introduce and motivate an evidence logic for an  agents faced with possibly contradictory evidence from different sources. The logic is based on a neighborhood semantics, where a neighborhood N indicates that the agent has reason to believe that the true state of the world lies in N.    Further notions of relative plausibility between worlds and beliefs based on the ordering are then defined in terms of this evidence structure.    The semantics invites a number of natural special cases, depending on how uniform we make the  evidence sets, and how coherent their total structure. I will give an overview of the main axiomatizations for different classes of models and discuss logics that describe  the dynamics of changing evidence, and the resulting language extensions.   I will also discuss some intriguing connections  with logics of belief revision.
This is joint work with Johan van Benthem and David Fernandez-Duque.

 

This Week in Logic at CUNY

Computational Logic Seminar
Tuesday, October 22, 2013 2:00 pm Graduate Center, rm, 3209
Speaker: Melvin Fitting Lehman College – CUNY Graduate Center
Title: Justification Logic Semantics: A Little New, but Mostly Old
Link: http://nylogic.org/talks/justification-logic-semantics-a-little-new-but-mostly-old

Possible world semantics was introduced for justification logic in 2005. Initially it was for the Logic of Proofs, but it quickly extended to “nearby” logics, and more slowly to a wider family. Eight years is a long time, and by now people may be generally familiar with the ideas without having gone through any of the details. I will try to remedy that.

Set theory seminar
Friday, October 25, 2013 10:00 am
Speaker: Erin Carmody The CUNY Graduate Center
Title: Killing Inaccessible Cardinals Softly
Link: http://nylogic.org/talks/killing-inaccessible-cardinals-softly

I shall introduce the killing-them-softly phenomenon among large cardinals by showing how it works for inaccessible and Mahlo cardinals. A large cardinal is killed softly whenever, by forcing, one of its large cardinal properties is destroyed while as many as possible weaker large cardinal properties, below this one, are preserved. I shall also explore the various degrees of inaccessibility and show Mahlo cardinals are alpha-hyperbeta-inaccessible and beyond.

Model theory seminar
Friday, October 25, 2013 12:30 pm
Speaker: Alf Dolich The City University of New York
Title: TBA
Link: http://nylogic.org/talks/tba-7

CUNY Logic Workshop
Friday, October 25, 2013 2:00 pm GC 6417
Speaker: Jim Schmerl University of Connecticut
Title: Automorphism Groups of Countable, Recursively Saturated Models of Peano Arithmetic
Link: http://nylogic.org/talks/title-tba-7

It is still unknown whether there are nonisomorphic countable recursively saturated models M and N whose automorphism groups Aut(M) and Aut(N) are isomorphic. I will discuss what has happenednover the last 20 years towards showing that such models do not exist, including some very recent results.

 

Set theory seminar
Friday, November 1, 2013 10:00 am GC 6417
Speaker: Karel Hrbacek City College of New York, CUNY
Title: Some problems motivated by nonstandard set theory
Link: http://nylogic.org/talks/some-problems-motivated-by-nonstandard-set-theory

Nonstandard set theory enriches the usual set theory by a unary “standardness” predicate. Investigations of its foundations raise a number of questions that can be formulated in ZFC or GB and appear open. I will discuss several such problems concerning elementary embeddings, ultraproducts, ultrafilters and large cardinals.

This Week in Logic at CUNY

Models of PA
Wednesday, October 16, 2013 6:30 pm GC 4214.03 
Speaker: Whanki Lee Queensborough Community College, CUNY
Title: Cofinal extensions of recursively saturated ordered structures
Link: http://nylogic.org/talks/cofinal-extensions-of-recursively-saturated-ordered-structures 

 

Set theory seminar
Friday, October 18, 2013 9:30 am GC 6417 Two talks for set theory seminar on this day
Speaker: Marcin Sabok Instytut Matematyczny Uniwersytetu Wrocławskiego, Instytut Matematyczny Polskiej Akademii Nauk
Title: Canonical Ramsey theory on Polish spaces
Link: http://nylogic.org/talks/canonical-ramsey-theory-on-polish-spaces 

I would like to give an overview of recent results in canonical Ramsey theory in the context of descriptive set theory. This is the subject of a recent monograph joint with with Vladimir Kanovei and Jindra Zapletal. The main question we address is the following. Given an analytic equivalence relation on a Polish space, can one find a large subset of the space on which it has a simple form? Canonical Ramsey theory stems from finite combinatorics and is concerned with finding canonical forms of equivalence relations on finite (or countable) sets. We obtain canonization results for analytic and Borel equivalence relations and in cases when canonization is impossible, we prove ergodicity theorems. For a publisher’s book description see:

http://www.youtube.com/watch?v=ZPXBcKeepKk
 

Kolchin seminar in Differential Algebra
Friday, October 18, 2013 10:15 am GC 5382 
Speaker: Tom Scanlon University of California – Berkeley
Title: D-Fields as a Common Formalism for Difference and Differential Algebra
Link: http://nylogic.org/talks/d-fields-as-a-common-formalism-for-difference-and-differential-algebra 

In a series of papers with Rahim Moosa, I have developed a theory of D-rings unifying and generalizing difference and differential algebra. Here we are given a ring functor D whose underlying additive group scheme is isomorphic to some power of the additive group. A D-ring is a ring R given together with a homomorphism f : R → D(R). A first motivating example is when D(R) = R[ε]/(ε2), so that the data of D-ring is that of an endomorphism σ:R → R and a σ-derivation ∂:R → R (that is, ∂(rs) = ∂(r)σ(s)+σ(r)∂(s)). Another example is when D(R) = R, where a D-ring structure is given by an endomorphism of R.

We develop a theory of prolongation spaces, jet spaces, and of D-algebraic geometry. With our most recent paper, we draw out the model theoretic consequences of this work showing that in characteristic zero, the theory of D-fields has a model companion, which we call the theory of D-closed fields, and that many of the refined model theoretic theorems (eg the Zilber trichotomy) hold at this level of generality. As a complement, we show that no such model companion exists in characteristic p under a mild hypothesis on D.

Set theory seminar
Friday, October 18, 2013 10:45 am GC 6417 
Speaker: Natasha Dobrinen University of Denver
Title: Survey on the structure of the Tukey theory of ultrafilters
Link: http://nylogic.org/talks/survey-on-the-structure-of-the-tukey-theory-of-ultrafilters 

The Tukey order on ultrafilters is a weakening of the well-studied Rudin-Keisler order, and the exact relationship between them is a question of interest.  In second vein, Isbell showed that there is a maximum Tukey type among ultrafilters and asked whether there are others.  These two questions are the main guiding forces of the current research.  In this talk, we present highlights of recent work of Blass, Dobrinen, Mijares, Milovich, Raghavan, Todorcevic, and Trujillo (in various combinations for various papers).  Further information about results mentioned in this talk can be found in a recent survey article by the speaker.
There will be two talks for the set theory seminar on this day.

Model theory seminar
Friday, October 18, 2013 12:30 pm GC6417 
Speaker: Lynn Scow Vassar College
Title: Ramsey Transfer Theorems
Link: http://nylogic.org/talks/tba-3 

We survey some of the known approaches to transfer a Ramsey theorem for one class of finite structures to another. We will isolate some easy consequences and point to further directions.

CUNY Logic Workshop
Friday, October 18, 2013 2:00 pm GC 6417 
Speaker: Paul B. Larson Miami University of Ohio
Title: Generic choice functions and ultrafilters on the integers
Link: http://nylogic.org/talks/generic-choice-functions-and-ultrafilters-on-the-integers 

We will discuss a question asked by Stefan Geschke, whether the existence of a selector for the equivalence relation E0 implies the existence of a nonprincipal ultrafilter on the integers. We will present a negative solution which is undoubtedly more complicated than necessary, using a variation of Woodin’s mathbbPmathrmmax. This proof shows that, under suitable hypotheses, if E is a universally Baire equivalence relation on the reals, with countable classes, then forcing over L(E,mathbbR) to add a selector for E does not add a nonprincipal ultrafilter on the integers.

Logic, Probability and Games, Logic and Games Seminar
Friday, October 18, 2013 2:00 pm GC 4419 
Speakers: Haim Gaifman (Columbia) and Rohit Parikh (CUNY)
Title: The Columbia-CUNY Workshop in Logic, Probability, and Games
Link: http://nylogic.org/talks/the-columbia-cuny-workshop-in-logic-probability-and-games 

There will be a meeting of this seminar on October 18 from 2 to 4 PM in room 4419.  Haim Gaifman (Columbia) and Rohit Parikh (CUNY) will speak.  Details will be announced next week.

This is a meeting of a joint CUNY-Columbia research group on Logic, Probability and Games.

Description: This workshop is concerned with applying formal methods to fundamental issues, with an emphasis on probabilistic reasoning decision theory and games. In this context “logic” is broadly interpreted as covering applications that involve formal representations. The topics of interest have been researched within a very broad spectrum of different disciplines, including philosophy (logic and epistemology), statistics, economics, and computer science. The workshop is intended to bring together scholars from different fields of research so as to illuminate problems of common interest from different perspectives. Throughout each academic year, meetings are regularly presented by the members of the workshop and distinguished guest speakers and are held alternatively at Columbia University and CUNY Graduate Center.

This Week in Logic at CUNY

Computational Logic Seminar
Tuesday, October 1, 2013 2:00 pm Graduate Center, rm. 3209
Speaker: Antonis Achilleos Graduate Center CUNY
Title: On the Complexity of Multi-agent Justification Logic Under Interacting Justifications
Link: http://nylogic.org/talks/on-the-complexity-of-multi-agent-justification-logic-under-interacting-justifications 

We introduce a family of multi-agent justification logics with interactions between the agents’ justifications, by extending and generalizing the two-agent versions of LP introduced by Yavorskaya in 2008. Known concepts and tools from the single-agent justification setting are adjusted for this multiple agent case. We present tableau rules and some preliminary complexity results: in several important cases, the satisfiability problem for these logics remains in the second level of the polynomial hierarchy, while for others it is PSPACE or EXP-hard.

 

Models of PA
Wednesday, October 2, 2013 6:30 pm GC 4214.03
Speaker: Roman Kossak The City University of New York
Title: Fullness
Link: http://nylogic.org/talks/fullness 

A model $M$ of PA is full if for every definable in $(M,omega)$ set $X$, $Xcap omega$ is coded in $M$. In a recent paper, Richard Kaye proved that $M$ is full if and only if its standard system is a model of full second order comprehension. Later in the semester we will examine Kaye’s proof. In this talk I will discuss some preliminary results and I will show an example of a model that is not full, using an argument that does not depend on Kaye’s theorem

 

Set theory seminar
Friday, October 4, 2013 10:00 am GC 6417
Speaker: Victoria Gitman The New York City College of Technology (CityTech), CUNY
Title: Embeddings among $\omega_1$-like models of set theory
Link: http://nylogic.org/talks/embeddings-among-omega_1-like-models-of-set-theory 

An $omega_1$-like model of set theory is an uncountable model, all of whose initial segments are countable. The speaker will present two $omega_1$-like models of set theory, constructed using $Diamond$, which are incomparable with respect to embeddability: neither is isomorphic to a submodel of the other. Under a suitable large cardinal assumption, there are such models that are well-founded.

Model theory seminar
Friday, October 4, 2013 12:30 pm GC6417
Speaker: David Marker University of Illinois at Chicago
Title: Real closures of $\omega_1$-like models of PA
Link: http://nylogic.org/talks/tba-5 

In an earlier seminar I showed that assuming diamond we can build many $omega_1$-like models of PA with the same standard system but non-isomorphic real closures. In this lecture I will show how to do this without diamond. This is joint work with Jim Schmerl and Charlie Steinhorn.

CUNY Logic Workshop
Friday, October 4, 2013 2:00 pm GC 6417
Speaker: Hans Schoutens The City University of New York
Title: Why model-theorists shouldn’t think that ACF is easy
Link: http://nylogic.org/talks/why-model-theorists-shouldnt-think-that-acf-is-easy

 

We all learned that stability theory derived many of its ideas from what happens in ACF, where everything is nice and easy. After all ACF has quantifier elimination and is strongly minimal, decidable, superstable, uncountably categorical, etc. However, my own struggles with ACF have humbled my opinion about it: it is an awfully rich theory that encodes way more than our current knowledge. I will discuss some examples showing how “difficult” ACF is: Grothendieck ring, isomorphism problem, set-theoretic intersection problem. Oddly enough, RCF seems to not have any of these problems. It is perhaps my ignorance, but I have come to think of RCF as much easier. Well, all, of course, is a matter of taste.

This Week in Logic at CUNY

Set theory seminar
Friday, September 27, 2013 10:00 am 6417
Speaker: Gunter Fuchs The City University of New York
Title: A self-specializing Souslin tree
Link: http://nylogic.org/talks/a-self-specializing-souslin-tree 

I will present a construction, assuming Jensen’s combinatorial principle diamond, of a Souslin tree T which, after forcing with T, will be Ahronszajn off the generic branch. More precisely, forcing with T will add a cofinal branch b through T, yet in the generic extension by b, whenever p is a node of T which does not belong to b, then the subtree of T which lies above p will be Q-embeddable, meaning that there is an order preserving function from that subtree to the rationals. This shows that the rigidity property of being Souslin off the generic branch is strictly stronger than the unique branch property, two notions of rigidty previously studied in joint work with Joel Hamkins, where it was conjectured that it would be possible to construct such a self specializing Souslin tree.

Model theory seminar
Friday, September 27, 2013 12:30 pm GC 6417
Speaker: Diana Ojeda Aristizabal Cornell University
Title: Finite forms of Gowers’ Theorem on the oscillation stability of c_0
Link: http://nylogic.org/talks/tba-4 

We give a constructive proof of the finite version of Gowers’ FIN_k Theorem and analyze the corresponding upper bounds. The FIN_k Theorem is closely related to the oscillation stability of c_0. The stabilization of Lipschitz functions on arbitrary finite dimensional Banach spaces was proved well before by V. Milman. We compare the finite FIN_k Theorem with the Finite Stabilization Principle found by Milman in the case of spaces of the form ell_{infty}^n, ninN, and establish a much slower growing upper bound for the finite stabilization principle in this particular case.

CUNY Logic Workshop
Friday, September 27, 2013 2:00 pm GC 6417
Speaker: Joel David Hamkins The City University of New York
Title: Satisfaction is not absolute
Link: http://nylogic.org/talks/satisfaction-is-not-absolute 

I will discuss a number of theorems showing that the satisfaction relation of first-order logic is less absolute than might have been supposed. Two models of set theory $M_1$ and $M_2$, for example, can agree on their natural numbers $langlemathbb{N},{+},{cdot},0,1,{lt}rangle^{M_1}=langlemathbb{N},{+},{cdot},0,1,{lt}rangle^{M_2}$, yet disagree on arithmetic truth: they have a sentence $sigma$ in the language of arithmetic that $M_1$ thinks is true in the natural numbers, yet $M_2$ thinks $negsigma$ there. Two models of set theory can agree on the natural numbers $mathbb{N}$ and on the reals $mathbb{R}$, yet disagree on projective truth. Two models of set theory can have the same natural numbers and have a computable linear order in common, yet disagree about whether this order is well-ordered. Two models of set theory can have a transitive rank initial segment $V_delta$ in common, yet disagree about whether this $V_delta$ is a model of ZFC. The theorems are proved with elementary classical methods.

This is joint work with Ruizhi Yang (Fudan University, Shanghai). We argue, on the basis of these mathematical results, that the definiteness of truth in a structure, such as with arithmetic truth in the standard model of arithmetic, cannot arise solely from the definiteness of the structure itself in which that truth resides; rather, it must be seen as a separate, higher-order ontological commitment.

Seminar in Logic and Games
Computational Logic Seminar
Giuseppe Longo,CNRS & Ecole Normale Supérieure, Paris
Schroedinger and Turing on the Logic of Life:  from the “coding” to the “genesis” of forms.
Friday, September 27, 2013, 2 PM, room 4421
Abstract: Schroedinger’s and Turing’s analyses of life phenomena have a twofold aspects. They both follow, first, a “coding paradigm”, of embryogenesis or of human computations and deductions respectively, and then move towards a more “dynamicist” approach. Schroedinger, in the second part of his 1944 book, hints to biological organization as negentropy – a variant of Gibbs dynamical analysis of energy – that we revitalized as anti-entropy, see references. Turing, after stressing that “the nervous system is surely not a Discrete State machine” (1950), invents the mathematics for an action/reaction/diffusion process, a “continuous system” (1952), where chemical matter (an hardware with no software) organizes itself along morphogenesis.
We will hint to the paths for thought opened by Turing’s dynamics as continuous deformations at the core of Turing’s pioneering paper of 1952, where symmetry breakings are a key component of the bio-chemical processes.