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Persistence and Atomic Generation for Varieties of Boolean Algebras with Operators

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Abstract

A variety V of Boolean algebras with operators is singleton-persistent if it contains a complex algebra whenever it contains the subalgebra generated by the singletons. V is atom-canonical if it contains the complex algebra of the atom structure of any of the atomic members of V.

This paper explores relationships between these "persistence" properties and questions of whether V is generated by its complex algebras or its atomic members, or is closed under canonical embedding algebras or completions. It also develops a general theory of when operations involving complex algebras lead to the construction of elementary classes of relational structures.

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  1. School of Mathematical and Computing Sciences, Victoria University, P.O. Box 600, Wellington, New Zealand

    Robert Goldblatt

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  1. Robert Goldblatt
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Goldblatt, R. Persistence and Atomic Generation for Varieties of Boolean Algebras with Operators. Studia Logica 68, 155–171 (2001). https://doi.org/10.1023/A:1012491022267

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