**Computational Logic Seminar**

** Tuesday, March 5, 2013 2:00 pm**

Speaker: Sergei Artemov The CUNY Graduate Center

Title: Lost in translation: a critical view of epistemic puzzles solutions.

There are two basic ways to specify an epistemic scenario:

1. Syntactic: a verbal description with some epistemic logic on the

background and some additional formalizable assumptions; think of the

Muddy Children puzzle.

2. Semantic: providing an epistemic model; think of Aumann structures

– a typical way to define epistemic components of games.

Such classical examples as Muddy Children, Wise Men, Wise Girls, etc.,

are given by syntactic descriptions (type 1), each of which is

“automatically” replaced by a simple finite model (type 2). Validity

of such translations from (1) to (2) will be the subject of our study.

We argue that in reducing (1) to (2), it is imperative to check

whether (1) is complete with respect to (2) without which solutions

of puzzles by model reasoning in (2) are not complete, at best. We

have already shown that such reductions can be justified in the Muddy

Children puzzle MC due to its model categoricity: we have proved that

MC has the unique “cube” model Q_n for each n. This fixes an obvious

gap in the “textbook” solution of Muddy Children which did not provide

a sufficient justification for using Q_n.

We also show that an adequate reduction of (1) to (2) is rather a

lucky exception, which makes the requirement to check the completeness

of (1) w.r.t. (2) necessary. To make this point, we provide a

simplified version of Muddy Children (by dropping the assumption “no

kid knows whether he is muddy”) which admits the usual deductive

solution by reasoning from the syntactic description, but which cannot

be reduced to any finite model.

**Models of PA**

** Wednesday, March 6, 2013 6:45 pm**

Speaker: Keita Yokoyama Mathematical Institute, Tohoku University

Title: Several versions of self-embedding theorem

In this talk, I will give several versions of Friedman’s

self-embedding theorem which can characterize subsystems of Peano

arithmetic. Similarly, I will also give several variations of Tanaka’s

self-embedding theorem to characterize subsystems of second-order

arithmetic.

**Set theory seminar**

** Friday, March 8, 2013 10:00 am**

Speaker: Robert Lubarsky Florida Atlantic University

Title: Forcing for Constructive Set Theory

As is well known, forcing is the same as Boolean-valued models. If

instead of a Boolean algebra one used a Heyting algebra, the result is

a Heyting-valued model. The result then typically models only

constructive logic and falsifies Excluded Middle. On the one hand,

many of the same intuitions from forcing carry over, while on the

other the result is quite foreign to a classical mathematician. I will

give a survey of perhaps too many examples, and call for the

importation of more methods from current classical set-theory into

constructivism.

Model theory seminar

Friday, March 8, 2013 12:30 pm

Speaker: Roman Kossak The City University of New York

Title: On strength of weakness

I will explain why countable models of PA which are just recursively

saturated do not have maximal automorphisms. If time permits I will

also show why recursive saturation implies standard system saturation

for models of rich theories.

**CUNY Logic Workshop**

** Friday, March 8, 2013 2:00 pm**

Speaker: Keita Yokoyama Mathematical Institute, Tohoku University

Title: Reverse mathematics for second-order categoricity theorem

It is important in the foundations of mathematics that the natural

number system is characterizable as a system of 0 and a successor

function by second-order logic. In other words, the following

Dedekind’s second-order categoricity theorem holds: every Peano system

$(P,e,F)$ is isomorphic to the natural number system $(N,0,S)$. In

this talk, I will investigate Dedekind’s theorem and other similar

statements. We will first do reverse mathematics over $RCA_0$, and

then weaken the base theory. This is a joint work with Stephen G.

Simpson.

**Models of PA**

** Wednesday, March 13, 2013 6:45 pm**

Speaker: Tin Lok Wong Ghent University

Title: Generalizing the notion of interstices

I will present a generalization of the notion of interstices that

originated from the study of generic cuts.

**Model theory seminar**

** Friday, March 15, 2013 12:30 pm**

Speaker: Philipp Rothmaler The City University of New York

Title: Stability revisited

I will discuss an observation Ivo Herzog and I made in the last

millennium that yields a purely topological definition of stability of

a complete first-order theory in terms of their Stone spaces.

**CUNY Logic Workshop**

** Friday, March 15, 2013 2:00 pm**

Speaker: Charles Steinhorn Vassar College

Title: TBA