Choiceless Löwenheim-Skolem property and uniform definability of grounds

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, without the axiom of choice, we show that if a certain downward Löwenheim-Skolem property holds then all grounds are uniformly definable. We also prove that the axiom of choice is forceable if and only if the universe is a small extension of some transitive model of ZFC.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2019 Apr 1

Keywords

  • Axiom of Choice
  • Forcing method
  • Set-theoretic geology

ASJC Scopus subject areas

  • General

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