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arXiv · 1305.3406

On Tense MV-algebras

Michal Botur·Jan Paseka
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Abstract

The main aim of this article is to study tense MV-algebras which are just MV-algebras with new unary operations $G$ and $H$ which express a universal time quantifiers. Tense MV-algebras were introduced by D. Diagonescu and G. Georgescu. Using a new notion of an fm-function between MV-algebras we \zruseno{will prove} \zmena{settle a half of their Open problem about representation for some classes of tense MV-algebras, i.e., we show} that any tense semisimple MV-algebra is induced by a time frame analogously to classical works in this field of logic. As a by-product we obtain a new characterization of extremal states on MV-algebras.

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Michal Botur, Jan Paseka. 2013-05-15. On Tense MV-algebras. https://arxiv.org/abs/1305.3406

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