*Computational Logic Seminar*

Time 2:00 – 4:00 PM, February 14, Room 3209

Speaker: Antonis Achilleos (Graduate Center)

Title: The complexity of multi-agent explicit knowledge II.

*Models of Peano Arithmetic*

Wednesday, February 15, 2012 6:30 pm Room 4214-03 ((Note: new day and time))

Professor Roman Kossak (The City University of New York)

More on open problems in Models of PA

*Set Theory Seminar*

Friday, February 17, 2012 10:00 am GC 6417

Ms. Erin K. Carmody (Ph.D. Program in Mathematics, Graduate Center of CUNY) Forcing Martin’s Axiom

Abstract. If V is a model of set theory, Martin’s Axiom is the assertion that if P is a partial order which satisfies the countable (anti)chain condition and D is a family of less than continuum many dense subsets of P, then there exists in V a D-generic filter on P. In a universe where the continuum hypothesis holds, Martin’s Axiom is true for arbitrary partial orders since we can always construct, in V, a filter on P which intersects countably many dense subsets. I will show the classical result that Martin’s Axiom is consistent with the continuum being a variety of sizes, other than the first uncountable cardinal. That is, I will show how to create the partial order which gives rise to a generic filter and a generic extension of V where Martin’s Axiom and the negation of the continuum hypothesis hold. In such a generic extension, Martin’s Axiom has many consequences regarding the real numbers. For example, a consequence of this axiom is that the continuum is regular and the power set of any cardinal less than continuum is also of size continuum. Also, Martin’s Axiom implies that the continuum is not real-valued measurable. This talk will provide a detailed look at the method of iterating ccc forcing to create a generic extension of a model of ZFC.

*Model Theory Seminar*

Friday, February 17, 2012 12:30 pm GC 6417

Mr. Whanki Lee (CUNY Graduate Center)

Chronically resplendent models and totally resplendent models.

*Logic Workshop*

Friday, February 17, 2012 2:00 pm GC 6417

Professor Philip Welch (University of Bristol)

Global Reflection Properties

Next Week in Logic at CUNY:

– – – – Monday, Feb 20, 2012 – – – –

– – – – Tuesday, Feb 21, 2012 – – – –

– – – – Wednesday, Feb 22, 2012 – – – –

– – – – Thursday, Feb 23, 2012 – – – –

– – – – Friday, Feb 24, 2012 – – – –

Model Theory Seminar

Friday, February 24, 2012 12:30 pm GC 6417

Professor Jouko Väänänen (University of Helsinki)

On second order model-theory I

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

Friday, February 24, 2012 2:00 pm GC 6417

Professor Simon Thomas (Rutgers University)

On the Steinhaus and Bergman Properties for infinite products of finite groups

Abstract. For each prime p, let SL(2,p) be the corresponding special linear group over the field with p elements. Then, by considering the ultraproduct with respect to any nonprincipal ultrafilter, it is easily seen that the full direct product Π SL(2,p) has countable cofinality. In recent joint work, Jindra Zapletal and I considered the question of whether the existence of a nonprincipal ultrafilter is either necessary or sufficient in order to prove this result. Perhaps surprisingly, the answer turned out to involve large cardinals, a suitable Ramsey theorem and the asymptotic representation theory of finite groups.

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