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.

中文翻译：

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作为代数系统的布尔值宇宙。II：内涵层次

正在研究的是集合论签名的布尔值代数系统的传递性、正则性和 σ -正则性的概念。引入了任意外延布尔值系统上的宇宙概念。通过各种层次结构对宇宙的结构提出了一些描述。结果用于证明布尔值宇宙的唯一性直至唯一同构。