Boolean orthoposets and two-valued states on them
type: Item
instance of: scholarly article
title: Boolean orthoposets and two-valued states on them
zbMATH Open document ID: 0791.03041
DOI: 10.1016/0034-4877(92)90021-R
author: Josef Tkadlec
published in: Reports on Mathematical Physics
publication date: 1994-07-07T00:00:00Z
review text: Let \(P\) be an orthoposet. If \(a\vee b=0\) \((a,b\in P)\) implies \(a\perp b\), we call \(P\) Boolean. A state (bounded non-negative measure) \(s\) on \(P\) is called Jauch-Piron if for every pair \(a,b\in P\) with \(s(a)=1=s(b)\) there is a \(c\in P\) with \(s(c)= 1\) such that \(c\leq a,b\). The author proves that: (i) Every orthoposet with a full set of two-valued Jauch-Piron states is Boolean, and (ii) Every atomic Boolean orthoposet has a full set of two-valued Jauch-Piron states. This is not true for orthomodular posets.
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 06C15
zbMATH DE Number: 459128
zbMATH Keywords: two-valued states
zbMATH Keywords: orthoposet
zbMATH Keywords: Jauch-Piron states
zbMATH Keywords: Boolean orthoposet
reviewed by: Vladimír Rogalewicz
MaRDI profile type: Publication
cites work: Q5551052
cites work: On the Representation of Boolean Orthomodular Partially Ordered Sets
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cites work: Q3981821
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cites work: Orthomodular structures as quantum logics. Transl. from the Slovak
cites work: λ NOTE ON DISTRIBUTIVITY IN ORTHOPOSETS
cites work: Boolean orthoposets---concreteness and orthocompleteness
full work available at URL: 0034-4877(92)90021-r
OpenAlex ID: W1992904107
description: scientific article; zbMATH DE number 459128