Wednesday, February 11, 20154:50 pmModels of PAGC 6300

# Models with the omega-property

## Roman Kossak

### The City University of New York

A model M of PA has the omega-property if it has an elementary end extension coding a subset

of M of order type omega. The countable short recursively saturated models are a proper subclass

of the countable models with the omega-property, and both classes share many common

model theoretic properties. For example, they all have automorphism groups of size continuum. I will give a brief survey of what is known about models with the omega-property and I will discuss some open problems.

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.