Boolean-Valued Universe as an Algebraic System. II: Intensional Hierarchies

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Under study are the notions of transitivity, regularity, and σ-regularity for Boolean-valued algebraic systems of set-theoretic signature. The notion of a universe over an arbitrary extensional Boolean-valued system is introduced. Some description is proposed for the structure of the universe by means of various hierarchies. The results are used for proving the uniqueness of a Boolean-valued universe up to a unique isomorphism.

Original languageEnglish
Pages (from-to)426-452
Number of pages27
JournalSiberian Mathematical Journal
Issue number3
Publication statusPublished - 1 May 2020


  • Boolean-valued algebraic system
  • Boolean-valued analysis
  • cumulative hierarchy
  • set theory
  • universe

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