# This Week in Logic at CUNY

Computational Logic Seminar
October 23, Time 2:00 – 4:00 PM, Room 3309.
Title: On tolerance analysis of games with belief revision

Abstract. Aumann’s Rationality Theorem claims that in perfect
information games, common knowledge of rationality yields backward
induction (BI). Stalnaker argued that in the belief revision setting,
BI did not follow from Aumann’s assumptions. However, as shown by
Artemov, if common knowledge of rationality is understood in the
robust sense, i.e., if players do not forfeit their knowledge of
rationality even hypothetically, then BI follows.

A more realistic epistemic model would bound the number of
hypothetical non-rational moves by player i that can be tolerated
without revising the belief in i’s rationality on future moves. We
show that in the presence of common knowledge of rationality, if n
hypothetical non-rational moves by any player are tolerated, then each
game of length less than 2n + 3 yields BI, and that this bound on the
length of model is tight for each n. In particular, if one error per
player is tolerated, i.e., n = 1, then games of length up to 4 are BI
games, whereas there is a game of length 5 with a non-BI solution.

Set Theory Seminar
Friday, October 26, 2012, 10:00am GC 6417
Speaker: Thomas Johnstone
Title: Preservation of DC delta by forcing with a closure point at delta
(continuation of last week’s talk: Definability of the ground model in
forcing extensions of ZF-models)

Abstract: Richard Laver [2007] showed that if M satisfies ZFC and G is
any M-generic filter for forcing P of size less than delta, then M is
definable in M[G] from parameter P(delta)^M. I will discuss a
generalization of this result for models M that satisfy ZF but only a
small fragment of the axiom of choice. This is joint work with
Victoria Gitman.

Definition (ZF). P*Q has closure point delta if P is well-orderable of
size at most delta and Q is be well-orderable here.)

Theorem: If M models ZF+DC_delta and P is forcing with closure point
delta, then M is definable in M[G] from parameter P(delta)^M.

Model Theory Seminar
Friday, October 26, 2012, 12:30pm-1:45pm, GC 6417
Surreal Numbers

Abstract: We will discuss the surreal numbers, definitions of surreal
arithmetic, and some examples.

Logic Workshop
Friday, October 26, 2012 2:00 pm GC 6417
Dr. Vincent Guingona (Notre Dame University)
Convex orderability in algebraic theories

Abstract: In this talk, we analyze algebraic structures such as
groups and valued fields using model theoretic notions. Specifically,
we use VC-minimality and convex orderability, two properties
restricting the complexity of definable sets in one variable, to
better understand these structures. One task is to characterize when
certain structures are VC-minimal, which is accomplished by relating
it to convex orderability. For example, we show that an ordered group
is VC-minimal if and only if it is convexly orderable if and only if
it is abelian and divisible. This work is joint with Joseph Flenner.