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

Posted by Dima Sinapova , part of the Logic Seminar.

At

Nov. 7, 2017, 4 p.m.

In

SEO 427

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.