**February 6**

Whan Ki Lee,
CUNY

**$\kappa$-like models**

This is a continuation of a talk from last semester.

A model $(M, < ,\ldots)$ is said to be $\kappa$-like if $|M| = \kappa$ but for all $a \in M$, $|\{x \in M \mid x < a\}| < \kappa$. Based on the paper, the theory of $\kappa$-like models of arithmetic by R. Kaye, we will identify some axiom schemes true in such models of $I\Delta_0$ and investigate their interesting properties.