**Computational Logic Seminar**

** December 4, Time 2:00 – 4:00 PM, Room 3309**

Speaker: Konstantinos Pouliasis, CUNY Graduate Center

Title: Extending Curry – Howard Isomorphism With Justifications

Abstract: In this talk we discuss JCalc – a typed lambda calculus in

the extension of Curry-Howard isomorphism appropriate for the {->}

fragment of Justification Logic. The system axiomatizes a dialogue

between two calculi: an intuitionistic and a classical one. The first

corresponds to a constructive theory T whereas the second to a

classical T’ that is assumed to provide intended semantics for T.

Justified necessity will be treated as a proof binding construct

between proofs in T and T’. We will mainly focus on the type system of

JCalc and then mention some first metatheoretic results as well as

possible applications.

**GC Philosophy Colloquium**

** December 5, 2012, 4:15 pm GC Room 9204**

http://web.gc.cuny.edu/philosophy/events/colloquium/12_fall.htm

Speaker: Juliette Kennedy, University of Helsinki

Title: Les Mots et Les Choses: Reading Gödel on Formalization

**Set Theory Seminar**

** Friday, November 30, 2012, 10:00am GC 6417**

Speaker: Erin Carmody, CUNY Graduate Center, (Oral Exam)

Title: The Laver Preparation

Abstract: I shall show how to make a supercompact cardinal kappa

indestructible for <kappa-directed closed forcing after the Laver

preparation. I will begin by defining and proving the existence of the

Laver function. Then, use the Laver function to define the Laver

preparation and show how to make kappa indestructible. Finally, I will

show how the preparation does not protect kappa from all <kappa-closed

forcing by adding a Kurepa tree and destroying even the measurability

of kappa.

**Model Theory Seminar**

** Friday, December 7, 2012, 12:30pm-1:45pm, GC 6417**

Alexei Kolesnikov (Towson University)

Generalized amalgamation, homology groups, and polygroupoids in model theory

Abstract: The talk will be an exposition of the series of papers by

John Goodrick, Byunghan Kim, and the speaker. The papers develop the

basics of homology theory in a model-theoretic context and connect it

with generalized amalgamation properties. This talk will introduce

definitions of homology groups H_n associated with a family of

“amalgamation functors” and establish the connection between the

failure of generalized amalgamation and non-triviality of the

appropriate homology groups. The last part of the talk will introduce

the canonical object witnessing the failure of generalized

amalgamation.

**Logic Workshop**

** Friday, December 7, 2012 2:00 pm GC 6417**

Prof. Natasha Dobrinen (University of Denver)

Ramsey theory and the Tukey types of ultrafilters

Stemming from the study of Moore-Smith convergence in topology, Tukey

types form a coarsening of the well-known Rudin-Keisler equivalence

classes. We give an overview of the structure of the Tukey types of

ultrafilters. Near the bottom of the hierarchy, where selective

ultrafilters reside, Ramsey theory becomes essential in finding the

exact structures of the Tukey types and the Rudin-Keisler types

(isomorphism classes) within them. We present some new

Ramsey-classification theorems for equivalence relations on barriers

of a large class of topological Ramsey spaces and their applications

to a fine analysis of the Rudin-Keisler types within Tukey types of

ultrafilters associated to these spaces. This is joint work with

Todorcevic. Time permitting, we also present some recent work of

Dobrinen on the Tukey types of generic non-p-points near the bottom of

the Tukey hierarchy.