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arXiv · 2011.12791

Algebraic properties of paraorthomodular posets

Ivan Chajda·Davide Fazio·Helmut Länger·Antonio Ledda·Jan Paseka
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Abstract

Paraorthomodular posets are bounded partially ordered set with an antitone involution induced by quantum structures arising from the logico-algebraic approach to quantum mechanics. The aim of the present work is starting a systematic inquiry into paraorthomodular posets theory both from an algebraic and order-theoretic perspective. On the one hand, we show that paraorthomodular posets are amenable of an algebraic treatment by means of a smooth representation in terms of bounded directoids with antitone involution. On the other, we investigate their order-theoretical features in terms of forbidden configurations. Moreover, sufficient and necessary conditions characterizing bounded posets with an antitone involution whose Dedekind-MacNeille completion is paraorthomodular are provided.

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BibTeXRIS

Ivan Chajda, Davide Fazio, Helmut Länger, Antonio Ledda, Jan Paseka. 2020-11-25. Algebraic properties of paraorthomodular posets. https://arxiv.org/abs/2011.12791

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