GEOLOGY OF SYMMETRIC GROUNDS

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Abstract

Let us say that a model of ZF is a symmetric ground if V is a symmetric extension of the model. In this paper, we investigate set-theoretic geology of symmetric grounds. Under a certain assumption, we show that all symmetric grounds of V are uniformly definable. We also show that if AC is forceable over V, then the symmetric grounds are downward directed.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2019 Dec 21

Keywords

  • Axiom of choice
  • Forcing method
  • Set-theoretic geology
  • Symmetric extension
  • Symmetric ground

ASJC Scopus subject areas

  • General

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