Friday, March 11, 20162:00 pmSet Theory DayGC 4102 (Science Center)

# Minimal models of second-order set theories

## Kameryn Williams

### The CUNY Graduate Center

Everyone knows that there is a least transitive model of ZFC. Is the same true for second-order set theories? The main result of this talk is that the answer is no for Kelley-Morse set theory. Another notion of minimality we will consider is being the least model with a fixed first-order part. We will see that no countable model of ZFC has a least KM-realization. Along the way, we will look at the analogous questions for GĂ¶del-Bernays set theory.

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.