Complete and atomic Tarski algebras

Archive for Mathematical Logic 58 (7-8):899-914 (2019)
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Abstract

Tarski algebras, also known as implication algebras or semi-boolean algebras, are the \-subreducts of Boolean algebras. In this paper we shall introduce and study the complete and atomic Tarski algebras. We shall prove a duality between the complete and atomic Tarski algebras and the class of covering Tarski sets, i.e., structures \, where X is a non-empty set and \ is non-empty family of subsets of X such that \. This duality is a generalization of the known duality between sets and complete and atomic Boolean algebras. We shall also analize the case of complete and atomic Tarski algebras endowed with a complete modal operator, and we will prove a duality for these algebras.

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Subordination Tarski algebras.Sergio A. Celani - 2019 - Journal of Applied Non-Classical Logics 29 (3):288-306.
Relational representation for subordination Tarski algebras.Sergio A. Celani - 2024 - Journal of Applied Non-Classical Logics 34 (1):75-96.

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Categories of frames for modal logic.S. K. Thomason - 1975 - Journal of Symbolic Logic 40 (3):439-442.

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