@article { Gutman20200308,
  author = "Gutman A.E.",
  title = "Boolean-valued universe as an algebraic system. II: Intensional hierarchies",
  journal = "Sib. Matem. Zh.",
  year = "2020",
  volume = "61",
  number = "3",
  pages = "539--571",
  doi = "10.33048/smzh.2020.61.305",
  language = "russian",
  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"
}