# This Week in Logic at CUNY

This Week in Logic at CUNY:

Computational Logic Seminar
Time 2:00 – 4:00 PM, April 17, 2012, Room 3209.
Title: The Power of Knowledge in Games

Abstract: We propose a theory of the interaction between knowledge and
games. Epistemic game theory is a well developed subject but there is
also a need for a theory of how some agents can affect the outcome of
a game by affecting the knowledge which other agents have and thereby
affecting their actions.

We concentrate on games of incomplete or imperfect information, and
study how conservative, moderate, or aggressive players might play
such games. We provide models for the behavior of a knowledge
manipulator who seeks to manipulate the knowledge states of active
players in order to affect their moves and to maximize her own payoff
even while she herself remains inactive.

This is joint work with Rohit Parikh (The Graduate Center and Brooklyn
College) and Andreas Witzel (NYU).

Set Theory Seminar
Friday, April 20, 2012 10:00 am GC 6417
Mr. Alexander Rapp (Ph.D. Program in Mathematics, Graduate Center of CUNY)
Cohen forcing adds a Souslin Tree

Abstract. It will be shown, using an argument of Todorcevic, that
Cohen forcing adds a Souslin tree. The result is due to Shelah.

Model Theory Seminar
Friday, April 20, 2012 12:30 pm GC 6417
Professor John Baldwin (University of Illinois at Chicago)
Axiomatic Set Theory and L_{omega_1,omega}

Abstract. In the late 1960’s model theory and axiomatic set theory
seemed to be inevitably intertwined. The fundamental notions of first
order stability theory are absolute. We describe the role of this fact
in the development of first order model theory independent from set
theory since the 1970’s. The role of extensions of ZFC in infinitary
logic is muddled. Important results are proved using weak extensions
of ZFC; the use is not in general proved essential. We expound the
following proof-scheme: 1) Prove an infinitary sentence is consistent
with ZFC. 2) Prove there is a model of set theory for which this
sentence is absolute. 3) Deduce the property it expresses is provable
in ZFC. We will describe how this technique implies the following
recent result: Theorem (Shelah) Let phi be a sentence of
L_{omega_1,omega}. a) If ‘algebraic closure’ fails exchange on models
of phi then phi has many models in aleph_1. b) If phi is
pseudo-minimal then it has model in the continuum. Here algebraic
closure’ and pseudo-minimal’ are modifications of classical notions
appropriate for the context.

Logic Workshop
Friday, April 20, 2012 2:00 pm GC 6417
Professor Ivo Herzog (Ohio State University)
Diophantine Sets of Representations

Abstract. Let k be a field of characteristic 0 and L the special
linear Lie algebra sl(2,k). The Lie algebra L acts by derivations on
the ring k[x,y] of polynomials in two variables. This L-representation
admits a direct sum decomposition of k[x,y] into the subspaces
k[x,y]_n of homogeneous polynomials of total degree n. We will prove
that if phi(v) is a positive-primitive formula in one free variable,
and k is recursively presented, then the subset { n | phi(k[x,y]_n) =
0} of the natural numbers is recursive.
This is joint work with S. L’Innocente.

Next Week in Logic at CUNY:

– – – – Monday, Apr 23, 2012 – – – –

Models of Peano Arithmetic
Monday, April 23, 2012 7:00 pm Room 4214-03
Mr. Thomas Ferguson (Ph.D. Program in Philosophy, Graduate Center of CUNY)
Isomorphic + and nonisomorphic x

– – – – Tuesday, Apr 24, 2012 – – – –

– – – – Wednesday, Apr 25, 2012 – – – –

– – – – Thursday, Apr 26, 2012 – – – –

– – – – Friday, Apr 27, 2012 – – – –

Set Theory Seminar
Friday, April 27, 2012 10:00 am GC 6417
Professor Thomas Johnstone (NYC College of Technology (CUNY))
The Definability of the Ground Model in Forcing Extensions

Logic Workshop
Friday, April 27, 2012 2:00 pm GC 6417
Professor Chris Miller (The Ohio State University)
Towards a foundation for tame control theory.

Abstract. Mathematical control theory is the area of
application-oriented mathematics that deals with the basic principles
underlying the analysis and design of control systems. There is a
natural division of control systems into two main types: discrete and
continuous. I will discuss how model-theoretic methods or points of
view might contribute to more abstract or foundational aspects of
continuous control via the study of expansions of o-minimal structures
on the real field by trajectories of definable vector fields.

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The majority of this information, including an interactive calendar of
future events, can be found at our website:

http://nylogic.org/Calendar