Countable Jauch-Piron logics
type: Item
instance of: scholarly article
title: Countable Jauch-Piron logics
zbMATH Open document ID: 0793.03070
DOI: 10.1007/BF01215295
author: Peter G. Ovchinnikov
published in: International Journal of Theoretical Physics
publication date: 1993-12-12T00:00:00Z
review text: The author shows that every orthomodular lattice with a finite- dimensional space of bounded finitely additive signed measures has a countable model (i.e., a countable subortholattice such that every finitely additive state on it can be uniquely extended to a finitely additive state on the given ortholattice). As a consequence (using the Gleason theorem) he gives examples of countable unital Jauch-Piron orthomodular lattices that are not Boolean (models of lattices of all subspaces of \(R^ n\), \(n>3\)). This remarkable result completes the result of \textit{V. Rogalewicz} [Int. J. Theor. Phys. 30, No. 4, 437-445 (1991; Zbl 0728.03034)], who proved that the number of blocks of a unital Jauch-Piron orthomodular poset is finite if and only if it equals 1. In the appendix an older result concerning the characterization of orthomodular posets by means of two-element and three-element partitions of unity is presented.
reviewed by: Josef Tkadlec
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 465575
zbMATH Keywords: Jauch-Piron logic
zbMATH Keywords: extension of states
zbMATH Keywords: orthomodular lattice
zbMATH Keywords: signed measures
zbMATH Keywords: orthomodular posets
MaRDI profile type: Publication
cites work: QUANTUM LOGICS WITH JAUCH–PIRON STATES
cites work: Q3245484
cites work: Q5551052
cites work: Q4750696
cites work: Q4100556
cites work: Orthomodular structures as quantum logics. Transl. from the Slovak
cites work: Jauch-Piron logics with finiteness conditions
cites work: Jauch–Piron states
description: scientific article; zbMATH DE number 465575