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.
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Dedicated to Yu. L. Ershov on the occasion of his 80th birthday.
Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 3, pp. 539–571.
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project 0314-2019-0005).
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Gutman, A.E. Boolean-Valued Universe as an Algebraic System. II: Intensional Hierarchies. Sib Math J 61, 426–452 (2020). https://doi.org/10.1134/S0037446620030052
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DOI: https://doi.org/10.1134/S0037446620030052