# This Week In Logic at CUNY

Computer Science Colloquium and Computational Logic Seminar
Thursday September 19, at 4:15, Room 3209
(NOTE: there will be no Seminar Meeting on Tuesday September 17)
Speaker: Rohit Parikh, Brooklyn College and the Graduate Center.
Title: Epistemic Logic, Games and Social Software: some old and new ideas

Abstract: Epistemic reasoning has gradually matured from being the domain of philosophers and logicians to becoming relevant also in economics and social science.  But theoretical computer science and game theory remain as two of the most powerful tools which epistemologists can wield.

Epistemic tools have been used by writers as different from each other as Shakespeare, Shaw and O’Henry.  Even the Indian epic Mahabharata contains stories whose main point is epistemic.

But more recently there has been technical work devoted to what might be called applied epistemic logic, and CUNY has been one of the leaders.  CUNY collaborators include Walter Dean, Cagil Tasdemir and Andreas Witzel.  Eric Pacuit, who got his doctorate from CUNY some years ago, has now become a household word in epistemic circles.  And Artemov’s own interest in Game theory has a very strong epistemic flavor.

There are also very important questions about the extent to which epistemic considerations enter into animal behavior.  Major figures like Peter Godfrey-Smith and Robert Lurz at CUNY have contributed to this field which began with some questions raised by Premack and Woodruff at U. Penn.

We cannot possibly do justice to all this work in a single talk but will try to give a bird’s eye view and indicate one or two “cute” results.

— Friday, September 20, 2013 —

Set theory seminar
Friday, September 20, 2013 10:00 am GC
Speaker: Joel David Hamkins The City University of New York
Title: The role of the axiom of foundation in the Kunen inconsistency

The axiom of foundation plays an interesting role in the Kunen inconsistency, the assertion that there is no nontrivial elementary embedding of the set-theoretic universe to itself, for the truth or falsity of the Kunen assertion depends on one’s specific anti-foundational stance.  The fact of the matter is that different anti-foundational theories come to different conclusions about this assertion.  On the one hand, it is relatively consistent with ZFC without foundation that the Kunen assertion fails, for there are models of  ZFC-F  in which there are definable nontrivial elementary embeddings $j:Vto V$. Indeed, in Boffa’s anti-foundational theory BAFA, the Kunen assertion is outright refutable, and in this theory there are numerous nontrivial elementary embeddings of the universe to itself. Meanwhile, on the other hand, Aczel’s anti-foundational theory GBC-F+AFA, as well as Scott’s theory GBC-F+SAFA and other anti-foundational theories, continue to prove the Kunen assertion, ruling out the existence of a nontrivial elementary embedding $j:Vto V$.

This is very recent joint work with Emil Jeřábek, Ali Sadegh Daghighi and Mohammad Golshani, based on an interaction growing out of Ali’s question on MathOverflow.  Our paper will be completed soon.

Model theory seminar
Friday, September 20, 2013 12:30 pm GC 6417
Speaker: Roman Kossak The City University of New York
Title: Resplendent and Transplendent Models
Link: http://nylogic.org/talks/resplendent-and-transplendent-modelsThis will be a more systematic overview of several topics mentioned by me an others in several talks last year. In particular, I will go over details of some basic arguments involving chronic resplendence.

CUNY Logic Workshop
Friday, September 20, 2013 2:00 pm
Speaker: Isaac Goldbring University of Illinois Chicago
Title: A survey of the model theory of tracial von Neumann algebras
Link: http://nylogic.org/talks/a-survey-of-the-model-theory-of-tracial-von-neumann-algebrasVon Neumann algebras are certain algebras of bounded operators on Hilbert spaces. In this talk we will survey some of the model theoretic results about (tracial) von Neumann algebras, focusing mainly on (in)stability, quantifier-complexity, and decidability. No prior knowledge of von Neumann algebras will be necessary. Some of the work presented is joint with Ilijas Farah, Bradd Hart, David Sherman, and Thomas Sinclair.