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Orthomodular lattices admitting no states. (English) Zbl 0219.06007


MSC:

06C15 Complemented lattices, orthocomplemented lattices and posets
06E99 Boolean algebras (Boolean rings)
05A99 Enumerative combinatorics
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References:

[1] Bennett, M. K., States on Orthomodular Lattices, J. Natur. Sci. and Math., VIII, 47-52 (1968) · Zbl 0167.28102
[2] Bennett, M. K., A Finite Orthomodular Lattice Which Does Not Admit a Full Set of States, SIAM Review, Vol. 12, No. 2, 267-271 (1970) · Zbl 0204.51802
[3] Dilworth, R. P., On Complemented Lattices, Tôhoku Math. J., 47, 18-23 (1940) · Zbl 0023.10202
[4] Greechie, R. J., On the Structure of Orthomodular Lattices Satisfying the Chain Condition, J. Combinatorial Theory, 4, 210-218 (1968) · Zbl 0157.03703
[5] Greechie, R. J., Orthomodular Lattices Admitting No State, (presented at AMS at Chicago. presented at AMS at Chicago, Illinois (April 17-20, 1968)), Abstract · Zbl 0219.06007
[6] Gudder, S. P., Spectral Methods for a Generalized Probability Theory, Trans. Amer. Math. Soc., 119, 428-442 (1965) · Zbl 0161.46105
[7] Gudder, S. P., Hilbert Space, Independence, and eneralized Probability, J. Math. Anal. Appl., 20, 48-61 (1967) · Zbl 0171.15602
[8] Holland, S. S., A Radon-Nikodym Theorem in Dimension Lattices, Trans. Amer. Math. Soc., 108, 66-87 (1963) · Zbl 0118.02501
[9] Janowitz, M. F., Quantifiers on Quasi-orthomodular Lattices, (Ph.D. Dissertation (1963), Wayne State University) · Zbl 0144.25303
[10] McLaren, M. D., Atomic Orthocomplemented Lattices, Pacific J. Math., 14, 597-612 (1964) · Zbl 0122.02201
[11] C. H. Randall; C. H. Randall
[12] Varadarajan, V. S., Probability in Physics and a Theorem on Simultaneous Observability, Comm. Pure Appl. Math., 15, 189-217 (1962) · Zbl 0109.44705
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