Logic Colloquium 2019, Prague, August 11 – 16, 2019

European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium ’19 will take place during August 11th–16th in Prague, Czech Republic.

Program Committee

Lev Beklemishev (Moscow, chair), Andrew Arana (Paris), Agata Ciabattoni (Vienna), Russell Miller (New York), Martin Otto (Darmstadt), Pavel Pudlák (Prague), Stevo Todorčević (Toronto), Alex Wilkie (Manchester)

Organizing Committee

David Chodounský (co-chair), Jonathan Verner (co-chair), Petr Cintula, Radek Honzík, Jan Hubička, Pavel Pudlák, Jan Starý, Neil Thapen

website

Piotr Koszmider: Uncountable constructions from CH using generic filters

Seminar: Working group in applications of set theory, IMPAN

Thursday, 11.10. 2018, 10:15, room 105, IMPAN

Speaker: Piotr Koszmider (IMPAN)

Title: “Uncountable constructions from CH using generic filters”

Abstact. We will present some old CH constructions due to S. Shelah. As usual they use transfinie induction, diagonalization and enumeration of all relevant objects in the first uncountable type. However, the use of the Martin’s axiom type arguments makes them additionally powerful.

Visit our seminar page which may include some future talks at https://www.impan.pl/~set_theory/Seminar/

Clinton Conley: Realizing abstract systems of congruence II

Mathematical logic seminar – Oct 9 2018
Time: 3:30pm – 4:30 pm

Room: Wean Hall 8220

Speaker: Clinton Conley
Department of Mathematical Sciences
CMU

Title: Realizing abstract systems of congruence II

Abstract:

An abstract system of congruence (ASC) is simply an equivalence relation
on the power set of a finite set F satisfying some nondegeneracy
conditions. Given such an ASC and an action of a group G on a set X, a
realization of the ASC is a partition of X into pieces indexed by F such
that whenever two subsets A, B are asc-equivalent, the corresponding
subsets XA and XB of X can be translated to one another in the action.
Familiar notions like paradoxical decompositions can be easily formalized
and refined by the ASC language. Wagon, upon isolating this notion,
characterized those ASCs which can be realized by rotations of the sphere.
He asks whether there is an analogous characterization for realizing ASCs
using partitions with the property of Baire. We provide such a
characterization. This is joint work with Andrew Marks and Spencer Unger.

Miha Habič: Surgery and generic coding

Dear all,

The seminar meets on Wednesday October 10th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Note that there will be no seminar on Wednesday October 17th.

Program: Miha Habič — Surgery and generic coding

There has been some interest recently in nonamalgamability phenomena
between countable models of set theory, and forcing extensions of a
fixed model in particular. Nonamalgamability is typically achieved by
coding some forbidden object between a collection of models in such a
way that each model on its own remains oblivious, but some combination
of them can recover the forbidden information.

In this talk we will examine the problem of coding arbitrary information
into a generic filter, focusing on two particular examples. First, I
will present some results of joint work with Jonathan Verner where we
consider surgical modifications to Cohen reals and sets of indices where
such modifications are always possible. Later, I will discuss a recent
result of S. Friedman and Hathaway where they achieve, using different
coding, nonamalgamability between arbitrary countable models of set
theory of the same height.

Best,
David

David Fernández-Bretón – Finiteness classes arising from Ramsey-theoretic statements in set theory without choice

Talk held by David Fernández-Bretón (KGRC) at the KGRC seminar on 2018-10-04. The recorded talk is available here.

Abstract: In the absence of the Axiom of Choice, there may be infinite sets for which certain Ramsey-theoretic statements – such as Ramsey’s or (appropriately phrased) Hindman’s theorem – fail. In this talk, we will analyse the existence of such sets, and their precise location within the hierarchy of infinite Dedekind-finite sets; independence proofs will be carried out using the Fränkel-Mostowski technique of permutation models.

This is joint work with Joshua Brot and Mengyang Cao.

Gabriel Fernandes: Tall cardinals in extender models

Tuesday, October 9, 2018, 15.00
Howard House 4th Floor Seminar Room, University of Bristol

Speaker: Gabriel Fernandes (University of Münster)

Title: Tall cardinals in extender models

Abstract:

Gitik proved under ¬0^sword that if κ is a measurable cardinal and 2^κ > λ ≥ κ^+ and λ is a regular cardinal then o^K(κ) ≥ λ, where K stands for the core model. In joint work with Ralf Schindler, in a attempt to generalize Gitik’s result to larger core models, we obtained for the case where V is an extender model a characterization of λ-tall cardinals in terms of the function o^K(). In the talk I will define λ-tall cardinals, o^K(), give an informal definition of the core model, state precisely the characterization we obtained and sketch its proof.

Nigel Pynn-Coates: Asymptotic valued differential fields and differential-henselianity

Seminar will meet at 4:30pm Monday next week.

Mathematical logic seminar – Oct 1 2018 – NOTE UNUSUAL DAY AND TIME!
Time: 4:30pm – 5:30 pm

Room: Wean Hall 8220

Speaker: Nigel Pynn-Coates
Department of Mathematics
UIUC

Title: Asymptotic valued differential fields and differential-henselianity

Abstract:

It is well known that henselianity plays a fundamental role in the algebra and model theory of valued fields. The notion of differential-henselianity, introduced by Scanlon and developed in further generality by Aschenbrenner, van den Dries, and van der Hoeven, is a natural generalization to the setting of valued differential fields. I will present three related theorems justifying the position that differential-henselianity plays a similarly fundamental role in the algebra of asymptotic valued differential fields, a class arising naturally from the study of Hardy fields and transseries, and that have potential applications to the model theory of such fields.

Victor Torres Perez: Combinatorial Principles without MA

Dear all,

The seminar meets on Wednesday October 3rd at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Victor Torres Perez — Combinatorial Principles without MA

Rado’s Conjecture (RC) in the formulation of Todorcevic is the statement
that every tree T that is not decomposable into countably many
antichains contains a subtree of cardinality ℵ_1 with the same property.
Todorcevic has shown the consistency of this statement relative to the
consistency of the existence of a strongly compact cardinal.
Todorcevic also showed that RC implies the Singular Cardinal Hypothesis,
a strong form of Chang’s Conjecture, the continuum is at most ℵ_2, the
negation of Box(θ) for every regular θ ≥ ω_2, etc. These implications
are very similar to the ones obtained from traditional forcing axioms
such as MM or PFA. However, RC is incompatible even with MA(ℵ_1).
In this talk we will take the opportunity to give an overview of our
results with different coauthors obtained in the last few years together
with recent ones, involving RC, certain weak square principles and
instances of tree properties. These new implications seem to continue
suggesting that RC is a good alternative to forcing axioms. We will
discuss to which extent this may hold true and where we can find some
limitations. We will end the talk with some open
problems and possible new directions.
For example, we will also discuss some recent results regarding the
P-ideal dichotomy (which can be consistent with the negation of MA(ℵ_1))
and square principles.

Best,
David

50 Years of Set Theory in Toronto, Fields institute, May 13-17, 2019

PRELIMINARY ANNOUNCEMENT

 

  50 Years of Set Theory in Toronto, May 13-17, 2019

This conference will celebrate  the 50th anniversary of the Toronto Set Theory Seminar. Its purpose is to introduce and/or survey contemporary work in the areas currently investigated by Seminar members. The conference will  take place at the Fields Institute in Toronto, and is supported by the Fields, NSF, and NSERC. Requests to be placed on the conference mailing list and other correspondence may  be directed to set-theory@Fields.utoronto.ca. Those who have already  written to the lead organizer asking to be placed on the mailing list need not write  again. The  conference  website is  http://www.fields.utoronto.ca/activities/18-19/set-theory. As planning proceeds, more information will  be posted there.

The local organizing committee consists of Franklin D. Tall (lead organizer), Ilijas Farah, Juris Steprans, Paul Szeptycki, Stevo Todorcevic, William Weiss.

There will be a separate event for graduates of the seminar on May 12th.

Clinton Conley: Realizing abstract systems of congruence

Mathematical logic seminar – Sep 25 2018
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         Clinton Conley
Department of Mathematical Sciences
CMU

Title:     Realizing abstract systems of congruence

Abstract:

An abstract system of congruence (ASC) is simply an equivalence relation on the power set of a finite set F satisfying some nondegeneracy conditions. Given such an ASC and an action of a group G on a set X, a realization of the ASC is a partition of X into pieces indexed by F such that whenever two subsets A, B are asc-equivalent, the corresponding subsets XA and XB of X can be translated to one another in the action. Familiar notions like paradoxical decompositions can be easily formalized and refined by the ASC language. Wagon, upon isolating this notion, characterized those ASCs which can be realized by rotations of the sphere. He asks whether there is an analogous characterization for realizing ASCs using partitions with the property of Baire. We provide such a characterization. This is joint work with Andrew Marks and Spencer Unger.