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Archive for Mathematical Logic

, Volume 57, Issue 7–8, pp 853–859 | Cite as

A model of \(\mathsf {ZFA}+ \mathsf {PAC}\) with no outer model of \(\mathsf {ZFAC}\) with the same pure part

  • Paul LarsonEmail author
  • Saharon Shelah
Article
  • 37 Downloads

Abstract

We produce a model of \(\mathsf {ZFA}+ \mathsf {PAC}\) such that no outer model of \(\mathsf {ZFAC}\) has the same pure sets, answering a question asked privately by Eric Hall.

Keywords

Set theory with atom Axiom of choice Forcing 

Mathematics Subject Classification

Primary 03E35 Secondary 03E25 03C75 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsMiami UniversityOxfordUSA
  2. 2.Department of MathematicsHebrew UniversityJerusalemIsrael

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