## Topological duality for Tarski algebras.(English)Zbl 1136.03046

Summary: In this paper we generalize the representation theory developed for finite Tarski algebras given in [S. A. Celani, “Modal Tarski algebras”, Rep. Math. Logic 39, 113–126 (2005; Zbl 1105.03069)]. We introduce the notion of Tarski space as a generalization of the notion of dense Tarski set, and we prove that the category of Tarski algebras with semi-homomorphisms is dually equivalent to the category of Tarski spaces with certain closed relations, called $$T$$-relations. By these results we obtain that the algebraic category of Tarski algebras is dually equivalent to the category of Tarski spaces with certain partial functions. We apply these results to give a topological characterization of the subalgebras.

### MSC:

 03G25 Other algebras related to logic 06E15 Stone spaces (Boolean spaces) and related structures

Zbl 1105.03069
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