Set theory seminarFriday, October 31, 201412:00 pmGC 6417

# Scott’s problem for models of ZFC

## Kameryn Williams

### The CUNY Graduate Center

Scott’s problem asks which Scott sets can be represented as standard systems of models of Peano arithmetic. Knight and Nadel proved in 1982 that every Scott set of cardinality $\le \omega_1$ is the standard system of some model of PA. Little progress has been made since then on the problem. I will present a modification of these results to models of ZFC and show that every Scott set of cardinality $\le \omega_1$ is the standard system of some model of ZFC. This talk will constitute the speaker’s oral exam.

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.

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on October 11th, 2014