## Logic Seminar

Paul Larson

Miami University

A model of ZFA with no outer model of ZFAC with the same pure part.

**Abstract:**We produce a model of ZFA (set theory with atoms) in which the Axiom of Choice holds for pure sets, but which has no cardinal-preserving outer model of Choice. The construction uses an infinitary sentence (introduced by Hjorth), having no model of cardinality $\aleph_{2}$, whose unique countable model is highly homogeneous. This is joint work with Saharon Shelah. This answers a question of Eric Hall.

Tuesday November 7, 2017 at 4:00 PM in SEO 427