## 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
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