This Week in Logic at CUNY


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
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

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.


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