Wednesday, October 5, 20166:30 pmModels of PAGC 4214-03

# Models of arithmetic with two expansions to $ACA_0$, Part 1

## Kameryn Williams

### The CUNY Graduate Center

In this talk and its sequel I will construct models of arithmetic with exactly two expansions to a model of $ACA_0$. To do so, I will use a modified version of Keisler’s construction of a rather-classless model. This talk will focus on this construction, while in Part 2 I will show how to use this construction to get the result.

Kameryn Williams is a graduate student in mathematics at the CUNY Graduate

Center, specializing in set theory and mathematical logic. He received a

bachelor’s degree in mathematics from Boise State University in 2012.