**Computational Logic Seminar**

** October 23, Time 2:00 – 4:00 PM, Room 3309.**

Speaker: Cagil Tasdemir, Graduate Center

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**

Shlomo Ben-Har (CUNY Graduate Center)

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.

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