author = "Gutman A.E.",

title = "Boolean-valued universe as an algebraic system. II: Intensional hierarchies",

journal = "Sib. Math. J.",

year = "2020",

volume = "61",

number = "3",

pages = "426--452",

doi = "10.1134/S0037446620030052",

annote = "For Boolean-valued algebraic systems of set-theoretic signature, the notions of transitivity, regularity, and $\sigma$-regularity are studied. The notion of a universe over an arbitrary extensional Boolean-valued system is introduced. A description is proposed of 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.",

keywords = "Boolean-valued algebraic system, set theory, Boolean-valued analysis, universe, cumulative hierarchy"