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Algebraic axiomatization of tense intuitionistic logic

Ivan Chajda (2011)

Open Mathematics

We introduce two unary operators G and H on a relatively pseudocomplemented lattice which form an algebraic axiomatization of the tense quantifiers “it is always going to be the case that” and “it has always been the case that”. Their axiomatization is an extended version for the classical logic and it is in accordance with these operators on many-valued Łukasiewicz logic. Finally, we get a general construction of these tense operators on complete relatively pseudocomplemented lattice which is a...

Algebras and spaces of dense constancies

Angelo Bella, Jorge Martinez, Scott D. Woodward (2001)

Czechoslovak Mathematical Journal

A DC-space (or space of dense constancies) is a Tychonoff space X such that for each f ∈ C ( X ) there is a family of open sets { U i i ∈ I } , the union of which is dense in X , such that f , restricted to each U i , is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean f -algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions...

Algebre di Łukasiewicz quasi-locali Stoneane

Francesco Lacava (2001)

Bollettino dell'Unione Matematica Italiana

We prove some properties of quasi-local Ł-algebras. These properties allow us to give a structure theorem for Stonean quasi-local Ł-algebras. With this characterization we are able to exhibit an example which provides a negative answer to the first problem posed in [4].

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