Topological duality for Tarski algebras |
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Authors: | Sergio A Celani Leonardo M Cabrer |
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Institution: | (1) CONICET and Departamento de Matemáticas, Facultad de Ciencias Exactas, Univ. Nac. del Centro, Pinto 399, 7000 Tandil, Argentina |
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Abstract: | In this paper we will generalize the representation theory developed for finite Tarski algebras given in 7]. We will introduce
the notion of Tarski space as a generalization of the notion of dense Tarski set, and we will 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 will obtain that the algebraic category of Tarski algebras is dually equivalent to the category
of Tarski spaces with certain partial functions. We will apply these results to give a topological characterization of the
subalgebras.
Received August 21, 2005; accepted in final form December 5, 2006. |
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Keywords: | 03G25 06E15 06F35 |
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