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

A. E. Gutman

doi:10.1134/S0037446620030052

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

A. E. Gutman

Mathematical Analysis Section

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	426-452
Number of pages	27
Journal	Siberian Mathematical Journal
Volume	61
Issue number	3
DOIs	https://doi.org/10.1134/S0037446620030052
Publication status	Published - 1 May 2020

Keywords

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

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10.1134/S0037446620030052

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