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Bulletin of the Australian Mathematical Society

An orthomodular poset which does not admit a normed orthovaluation

Peter D. Meyer, Peter D. Finch

Published Oct 1, 1970• 4 citations
Publisher

Abstract

It is of relevance to studies in the logic of quantum mechanics whether or not every separable completely orthomodular poset admits a normed σ-ortho-valuation. A finite orthomodular poset is constructed which is a counter-example to this proposition.
DOI
10.1017/s0004972700045822

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Previous article Next article A Finite Orthomodular Lattice Which Does Not Admit a Full Set of StatesMary Katherine BennettMary Katherine Bennetthttps://doi.org/10.1137/1012047PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Garrett Birkhoff and , John von Neumann, The logic of quantum mechanics, Ann. of Math. (2), 37 (1936), 823–843 MR1503312 0015.14603 CrossrefGoogle Scholar[2] Samuel S. Holland, Jr., J. Abbott, The current interest in orthomodular latticesTrends in Lattice Theory (Sympos., U.S. Naval Academy, Annapolis, Md., 1966), Van Nostrand Reinhold, New York, 1970, 41–126 MR0272688 Google Scholar[3] A. N. Kolmogorov, Foundations of the theory of probability, Chelsea Publishing Co., New York, 1956viii+84 MR0079843 0074.12202 Google Scholar[4] George W. Mackey, The mathematical foundations of quantum mechanics: A lecture-note volume, W., A. Benjamin, Inc., New York-Amsterdam, 1963x+137 MR0155567 0114.44002 Google Scholar[5] C. Randall, A Mathematical Foundation for Empirical Science with Special Reference to Quantum Theory. Part I: A Calculus of Experimental Propositions, Tech. Rep., KAPL-3147, Knolls Atomic Power Laboratory, 1966 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Noncontextual coloring of orthogonality hypergraphsJournal of Mathematical Physics, Vol. 63, No. 3 | 1 Mar 2022 Cross Ref Bibliography on quantum logics and related structuresInternational Journal of Theoretical Physics, Vol. 31, No. 3 | 1 Mar 1992 Cross Ref Orthomodular Lattices and Quadratic Spaces: A SurveyRocky Mountain Journal of Mathematics, Vol. 21, No. 3 | 1 Sep 1991 Cross Ref Automorphism groups and the full state spaces of the Petersen graph generalizations of G32Discrete Mathematics, Vol. 70, No. 2 | 1 Jan 1988 Cross Ref BACK MATTERMeasures and Hilbert Lattices | 29 May 2013 Cross Ref SPIN MANUALS: EMPIRICAL LOGIC TALKS QUANTUM MECHANICSMathematical Foundations of Quantum Theory | 1 Jan 1978 Cross Ref Some results from the combinatorial approach to quantum logicSynthese, Vol. 29, No. 1-4 | 1 Dec 1974 Cross Ref BIBLIOGRAPHYResiduation Theory | 1 Jan 1972 Cross Ref Orthomodular lattices admitting no statesJournal of Combinatorial Theory, Series A, Vol. 10, No. 2 | 1 Mar 1971 Cross Ref Volume 12, Issue 2| 1970SIAM Review175-324 History Submitted:31 October 1967Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1012047Article page range:pp. 267-271ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics