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http://dx.doi.org/10.4134/CKMS.2012.27.1.047

DISCRETE DUALITY FOR TSH-ALGEBRAS  

Figallo, Aldo Victorio (Departamento de Matem atic Universidad Nacional del Sur, Instituto de Ciencias Basica Universidad Nacional de San Juan)
Pelaitay, Gustavo (Departamento de Matematic Universidad Nacional del Sur, Instituto de Ciencias Basica Universidad Nacional de San Juan)
Sanza, Claudia (Departamento de Matematic Universidad Nacional del Sur, Instituto de Ciencias Basica Universidad Nacional de San Juan)
Publication Information
Communications of the Korean Mathematical Society / v.27, no.1, 2012 , pp. 47-56 More about this Journal
Abstract
In this article, we continue the study of tense symmetric Heyting algebras (or TSH-algebras). These algebras constitute a generalization of tense algebras. In particular, we describe a discrete duality for TSH-algebras bearing in mind the results indicated by Or lowska and Rewitzky in [E. Orlowska and I. Rewitzky, Discrete Dualities for Heyting Algebras with Operators, Fund. Inform. 81 (2007), no. 1-3, 275-295] for Heyting algebras. In addition, we introduce a propositional calculus and prove this calculus has TSH-algebras as algebraic counterpart. Finally, the duality mentioned above allowed us to show the completeness theorem for this calculus.
Keywords
symmetric Heyting algebras; tense operators; frames; discrete duality;
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