Wednesday, October 2, 20136:30 pmModels of PAGC 4214.03

# Fullness

## Roman Kossak

### The City University of New York

A model $M$ of PA is full if for every definable in $(M,omega)$ set $X$, $Xcap omega$ is coded in $M$. In a recent paper, Richard Kaye proved that $M$ is full if and only if its standard system is a model of full second order comprehension. Later in the semester we will examine Kaye’s proof. In this talk I will discuss some preliminary results and I will show an example of a model that is not full, using an argument that does not depend on Kaye’s theorem

Roman Kossak is professor of mathematics at The City University of New York, at Bronx Community College and also at the CUNY Graduate Center. He conducts research in mathematical logic, especially in model theory of Peano Arithmetic.