This Week in Logic at CUNY

 

Models of Peano Arithmetic
Monday, February 27, 2012 7:00 pm Room 4214-03
Professor Erez Shochat (St. Francis College)
Automorphism groups of saturated models of PA

Abstract. In this talk we survey recent results of Nurkhaidarov and
Schmerl concerning the automorphism groups or saturated models of PA.

 

Computational Logic Seminar
Time 2:00 – 4:00 PM, Room 3209, February 28
Speaker: Melvin Fitting (CUNY)
Title: Possible World Semantics for First Order LP

Abstract: In work of Artemov and Yavorskaya an elegant formulation of
the fi rst-order logic of proofs was given, FOLP. This logic plays a
fundamental role in providing an arithmetic semantics for fi rst-order
intuitionistic logic, as they showed. In particular, they proved an
arithmetic soundness theorem, and a realization theorem for FOLP.
Continuing with the study of FOLP, we provide a possible-world
semantics, based on our earlier propositional semantics for LP. We
also give an Mkrtychev semantics. We will present the semantics in
detail, but only sketch the completeness argument itself, since it is
a straightforward extension of familiar methods.

 

Set Theory Seminar
Friday, March 2, 2012 10:00 am GC 6417
Professor Dimitris Vlitas
An Infinite self dual Theorem

Abstract. Recall that the classical Ramsey theorem states that given
any finite coloring of the set of all K elements subsets of \omega
there exists of an infinite subset A \subseteq \omega where the
restriction of the coloring is constant. The dual form of Ramsey
theorem, the Carlson-Simpson Theorem, states that given any finite
Borel coloring of the set of all partitions of \omega into K many
classes, there exists a partition r of \omega into \omega many classes
such that the set of all K partitions of \omega resulting by
identifying classes of r is monochromatic. There are also the
corresponding finite versions of these results, the finite Ramsey
Theorem, and the Graham-Rothschild theorem, respectively. S. Solecki
recently proved a self dual theorem that implies simultaneously the
finite version of the Ramsey theorem and the Graham-Rothschild
theorem. He achieved that by introducing the notion of a connection,
which roughly speaking is a labelled partition of L into K many
classes, for K and L integers. He then proved that given any positive
integers K,L and M there exists N such that for any L coloring of all
labelled partitions of N into K many pieces, there exists a labelled
partition of M into K pieces, such that the set of all labelled
partitions of N into M composed with the particular labelled partition
of M into K is monochromatic. The composition is defined in the most
natural way by composing partitions, namely that partition N into M
pieces and then M into K pieces, so we finally partition N into K. The
composition of the label functions is done in the reverse order. We
extend canonically his notion of connection to labeled partitions of
\omega, with finite or infinitely many classes and we prove the
following: For any finite Borel coloring of all labelled K-partitions
of \omega there is a fixed labelled \omega-partition of \omega such
that the set of all of its reductions, ie labelled K-partitions of
\omega which result from putting pieces of the fixed partition
together, is monochromatic. The proof is done by induction on K and
the use of the left variable Hales-Jewett Theorem. In the final
section of the paper we extend this result by building the
corresponding topological Ramsey space F_{\omega,\omega}.

Model Theory Seminar
Friday, March 2, 2012 12:30 pm GC 6417
Professor Jouko Väänänen (University of Helsinki and University of Amsterdam)
On second-order model theory II

Abstract. This mini course will cover the following topics: second
order characterizable structures, Henkin models, Completeness Theorem,
internal categoricity, and existence of second order equivalent
non-isomorphic models.

Logic Workshop + Model Theory, Number Theory, Algebraic Geometry Umbrella series
Friday, March 2, 2012 2:00 pm GC 6417
Professor Zoe Chatzidakis (Université Paris 7)
Algebraic dynamics, difference fields and model theory

Abstract. In this talk I will discuss how to obtain the following result:
Let K_1, K_2 be algebraically closed fields intersecting in K (and
contained in some large algebraically closed field Omega), and for
i=1,2, let V_i be a variety defined over K_i, and f_i a dominant
rational map of V_i to V_i, with deg(f_2)>1. Viewing the V_i’s as
varieties defined over some algebraically closed L containing K_1 and
K_2, assume that there is a dominant rational map h from V_1 to V_2,
such that f_2h=hf_1.
Then there is a variety V defined over K, a dominant rational map f
from V to V, and a dominant rational map g from V_2 to V such that
fg=gf_2, and with deg(f)=deg(f_2).
This can be summarized as follows: if the algebraic dynamics (V_1,f_1)
defined over K_1 dominates the algebraic dynamics (V_2,f_2) defined
over K_2 and with deg(f_2)>1, then (V_2,f_2) dominates some (V,f)
defined over K and with deg(f)=deg(f_2).
Some precisions on the terminology: my varieties are irreducible,
affine or projective. An interesting case is when K_1=K.
The mysterious model-theoretic result from which the result follows,
is the following:
Let T be a theory which is supersimple and has the CBP. Let K_1 and
K_2 be algebraically closed subsets of a model M, intersecting in K,
a_1, a_2 tuples in M.
Assume that a_1 is independent from K_2 over K_1, a_2 is independent
from K_1 over K_2 and of finite rank over K_2. Assume furthermore that
tp(K_2/K) is almost p-internal, p a type of rank 1 over K, and that
a_2 is in acl(K_1K_2a_1). Then there is a_3 in dcl(K_2 a_2) which is
independent from K_2 over K, and such that tp(a_2/Ka_3) is almost
p-internal.
I will not explain the hypotheses on T, nor the proof of this result.
Let me just say that the theory of any existentially closed difference
field (Omega,\sigma) satisfy the hypotheses. I will explain how,
taking p to be a 1-type containing \sigma(x)=x, and translating the
algebraic dynamics problem into a problem about difference fields, one
obtains the result.
Recall that tp(K_2/K) is almost p-internal means that there is some L
independent from K_2 over K, and a set b of realisations of p, such
that K_2 is contained in acl(Lb).
When deg(f_2)=1, a similar result holds: (V_2,f_2) has a quotient
(V,f) defined over K (with dim(V)>1), but the proof is completely
different. I will not speak about this case (Jt with E. Hrushovski).

This is a joint talk with the CUNY Logic Workshop

Next Week in Logic at CUNY:

– – – – Monday, Mar 5, 2012 – – – –

– – – – Tuesday, Mar 6, 2012 – – – –

Computational Logic Seminar
Time 2:00 – 4:00 PM, Room 3209, March 6
Speaker: Cagil Tasdemir (Graduate Center)
Title: (provisional) Distributed Knowledge Authorization Language.

– – – – Wednesday, Mar 7, 2012 – – – –

Model Theory, Number Theory, Algebraic Geometry Umbrella series
Wednesday, March 7, 2012 4:30 pm Room C201
MONTAGU / Spring2012 + Model Theory Seminar / Spring2012
Dr. Ivan Tomasić (Queen Mary, University of London)
A twisted theorem of Chebotarev

Abstract. We will discuss a function field version of a theorem of
Chebotarev describing the distribution of local Frobenius elements
associated with a Galois covering of difference-algebraic varieties.
The result is stated in a shape of a trace formula, and one crucial
ingredient is Hrushovski’s twisted Lang-Weil estimate for the number
of points of a difference variety over the algebraic closure of a
finite field with a power of Frobenius. We will also give a general
description of definable sets over fields with Frobenius in terms of
twisted Galois covers.

MONTAGU is an interdisciplinary seminar organized by Roman Kossak,
Philipp Rothmaler, Hans Schoutens, and Lucien Szpiro

– – – – Thursday, Mar 8, 2012 – – – –

– – – – Friday, Mar 9, 2012 – – – –

CONFERENCE: Spring 2012 Mid-Atlantic Mathematical Logic Seminar
For talk abstracts and further details visit the website:
http://nylogic.org/MAMLS_GC_2012/MAMLS_GC_2012/MAMLS_GC_2012_talks

Friday, March 9, 2012 1:00 pm GC 4102 (Science Center)
Professor Mariya Soskova (Sofia University Faculty of Mathematics
and Informatics)
Extensions of the Turing model for relative definability

Friday, March 9, 2012 2:00 pm GC 4102 (Science Center)
Dr. David Aspero (University of Vienna, Insitute for Logic)
Wishful thinking in set theory: Omega-completeness and maximality

Friday, March 9, 2012 3:30 pm GC 4102 (Science Center)
Professor Jouko Väänänen (University of Helsinki and University of Amsterdam)
Sort Logic and Foundations of Mathematics

Friday, March 9, 2012 4:45 pm GC 4102 (Science Center)
Panel discussion: the unity and diversity of logic
The panelists will be Prof. Gregory Cherlin, Prof. Joel David Hamkins,
Prof. Rohit Parikh, and Prof. Jouko Väänänen, with the discussion
moderated by Prof. Russell Miller. Questions and participation from
the audience are encouraged.

– – – – Friday, Mar 9, 2012 – – – –

CONFERENCE: Spring 2012 Mid-Atlantic Mathematical Logic Seminar
For talk abstracts and further details visit the website:
http://nylogic.org/MAMLS_GC_2012/MAMLS_GC_2012/MAMLS_GC_2012_talks

Saturday, March 10, 2012 10:00 am Baruch College – Room 4120 VC
Professor Jan Reimann (Pennsylvania State University)
Degree-invariant functions and uniform Borel reductions

Saturday, March 10, 2012 11:00 am Baruch College – Room 4120 VC
Professor Henry Towsner (University of Connecticut)
Extracting information from proofs of sentences with set quantifiers

Saturday, March 10, 2012 2:00 pm Baruch College – Room 4120 VC
Professor Juliette Kennedy (University of Helsinki)
Change the logic, change the meaning? Quine’s dictum, formalism
freeness, and inner models from extended logics

Saturday, March 10, 2012 3:00 pm Baruch College – Room 4120 VC
Professor Karen Lange (Wellesley College)
Degrees of orderings on torsion-free abelian groups

Saturday, March 10, 2012 4:30 pm Baruch College – Room 4120 VC
Professor Gregory Cherlin (Rutgers University)
Metrically homogeneous graphs

– – – – Other Logic News – – – –

Introducing MONTAGU, the Model Theory, Number Theory, Algebraic
Geometry Umbrella series
http://nylogic.org/MONTAGU

The Model Theory, Number Theory and Algebraic Geometry Umbrella
seminar (aka MONTAGU) is a newly launched collaborative seminar which
will feature special, interdisciplinary events, connecting
model-theory and logic with algebraic and arithmetic number theory.
Events will be sponsored by the Model Theory Seminar, the Commutative
Algebra and Algebraic Geometry (CAAG) seminar and the Joint Number
Theory Seminar. This seminar is organized by Roman Kossak, Philipp
Rothmaler, Hans Schoutens, and Lucien Szpiro.

See events Friday, March 2nd and Wednesday, March 7th.

– – – – Web Site – – – –

The majority of this information, including an interactive calendar of
future events, can be found at our website:

http://nylogic.org/Calendar

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