Persistence and atomic generation for varieties of Boolean algebras with operators

Studia Logica 68 (2):155-171 (2001)
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.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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Reprint years 2004
DOI 10.1023/A:1012491022267
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Algebraic Logic, Where Does It Stand Today?Tarek Sayed Ahmed - 2005 - Bulletin of Symbolic Logic 11 (4):465-516.
Atomless Varieties.Yde Venema - 2003 - Journal of Symbolic Logic 68 (2):607-614.
Omitting Types for Algebraizable Extensions of First Order Logic.Tarek Sayed Ahmed - 2005 - Journal of Applied Non-Classical Logics 15 (4):465-489.

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