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Orthogonality spaces and atomistic orthocomplemented lattices
Czechoslovak Mathematical Journal, Tome 41 (1991) no. 1, pp. 8-23
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DOI : 10.21136/CMJ.1991.102428
Classification : 06C15, 81P10 
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Hedlíková, Jarmila; Pulmannová, Sylvia. Orthogonality spaces and atomistic orthocomplemented lattices. Czechoslovak Mathematical Journal, Tome 41 (1991) no. 1, pp. 8-23. doi: 10.21136/CMJ.1991.102428

[1] I. Amemiya H. Araki: A remark on Piron's paper. Publ. Research Inst. Math. Sci. Kyoto Univ. Series A 2 (1966) 423-427. | DOI | MR

[2] G. Birkhoff: Lattice theory. Coll. Publ. 25, Amer. Math. Soc., Providence, 3rd ed., 1967. | MR | Zbl

[3] G. Cattaneo G. Marino: Completeness of inner product spaces with respect to splitting subspaces. Letters in Math. Physics 11 (1986) 15-20. | DOI | MR

[4] A. Dvurečenskij: Completeness of inner product spaces and quantum logic of splitting subspaces. Letters in Math. Physics 15 (1988) 231 - 235. | DOI | MR

[5] A. Dvurečenskij: States on families of subspaces of pre-Hilbert spaces. Letters in Math. Physics 17 (1989) 19-24. | DOI | MR

[6] P. D. Finch: Orthogonality relations and orthomodularity. Bull. Austral. Math. Soc. 2 (1970) 125-128. | DOI | MR | Zbl

[7] D. J. Foulis C. H. Randall: Lexicographic orthogonality. J. Combinatorial Theory Ser. A 11 (1971) 157-162. | DOI | MR

[8] R. Goldblatt: Orthomodularity is not elementary. Journal Symbolic Logic 49 (1984)401-404. | MR | Zbl

[9] H. Gross H. A. Keller: On the definition of Hilbert space. Manuscripta Math. 23 (1977) 67-90. | DOI | MR

[10] S. P. Gudder: Projective representations of quantum logics. Internat. J. Theoret. Physics 3 (1970) 99-108. | DOI | MR

[11] S. Gudder: Inner product spaces. Amer. Math. Monthly 81 (1974) 29-36. | DOI | MR | Zbl

[12] S. Gudder: Correction to: „Inner product spaces". Amer. Math. Monthly 82 (1975) 251-252. | MR

[13] S. Gudder S. Holland: Second correction to: „Inner product spaces". Amer. Math. Monthly 82 (1975) 818. | DOI | MR

[14] W. Guz: Filter theory and covering law. Ann. Inst. H. Poincarè Sec. A Phys. Thèor. 29 (1978) 357-378. | MR | Zbl

[15] J. Hamhalter P. Pták: A completeness criterion for inner product spaces. Bull. London Math. Soc. 19 (1987) 259-263. | DOI | MR

[16] L. Iturrioz: Orthomodular ordered sets and orthogonal closure spaces. Portugal. Math. 39 (1980) 477-488. | MR

[17] G. Kalmbach: Orthomodular lattices. Academic Press, London, 1983. | MR | Zbl

[18] M. D. MacLaren: Atomic orthocomplemented lattices. Pacific J. Math. 14 (1964) 597-612. | DOI | MR | Zbl

[19] F. Maeda S. Maeda: Theory of symmetric lattices. Springer-Verlag, Berlin 1970. | MR

[20] C. Piron: Foundations of quantum physics. Benjamin, Reading, Massachusetts, 1976. | MR | Zbl

[21] R. Piziak: Orthomodular posets from sesquilinear forms. J. Austral. Math. Soc. 15 (1973) 265-269. | DOI | MR | Zbl

[22] S. Pulmannová: Superpositions of states and a representation theorem. Ann. Inst. H. Poincarè Sec. A Phys. Thèor. 32 (1980) 351-360. | MR

[23] S. Pulmannová: Transition probability spaces. J. Math. Physics 27 (1986) 1791-1795. | DOI | MR

[24] V. S. Varadarajan: Geometry of quantum theory. 2nd ed., Springer-Verlag, New York, 1985. | MR | Zbl

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