Orthocomplemented posets with a symmetric difference
type: Item
instance of: scholarly article
title: Orthocomplemented posets with a symmetric difference
zbMATH Open document ID: 1201.06006
author: Milan Matoušek
author: Pavel Pták
published in: Order
publication date: 2009-05-04T00:00:00Z
review text: The authors endow an orthocomplemented poset with a binary operation which models a symmetric difference of posets. The class of such posets is denoted by ODP. It is shown that any ODP is orthomodular. Then the authors deal with the question of when an ODP is set-representable. In general, this is not the case, and the authors characterize the positive case. It is shown that set-representability can be characterized in terms of two-valued morphisms, and it is proved that they form a quasivariety. Finally, they investigate when an orthomodular poset can be endowed with a symmetric difference. It is shown that not every orthomodular poset has this property.
reviewed by: Anatolij Dvurečenskij
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 5550514
zbMATH Keywords: orthomodular poset
zbMATH Keywords: quantum logic
zbMATH Keywords: symmetric difference
zbMATH Keywords: Boolean algebra
zbMATH Keywords: quasivariety
zbMATH Keywords: Frink ideal
MaRDI profile type: Publication
full work available at URL: s11083-008-9102-8
OpenAlex ID: W2006962118
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DOI: 10.1007/S11083-008-9102-8
description: scientific article; zbMATH DE number 5550514