Wednesday, November 4, 20156:30 pmModels of PAGC 4214-03

# Cofinal elementary extensions

## Whan Ki Lee

### Queensborough Community College, CUNY

We will discuss two weak versions of recursive saturation: K-tallness and tallness. K-tallness characterizes the countable models of *IΔ _{0} + exp* that have cofinal elementary extensions enlarging any infinite definable set, and tallness characterizes such models of linear ordering without the last element. I will present the proof of the latter. If time permits, we will also discuss the two properties in relation to the existence of

*κ*-pseudosaturated cofinal elementary extensions. Here,

*κ*-pseudosaturated structures are the structures all of whose infinite definable sets have a cardinality

*≥κ*.