[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 10.2977/prims/1195195769 | MR 0213266

[2] G. Birkhoff: Lattice theory. Coll. Publ. 25, Amer. Math. Soc., Providence, 3rd ed., 1967. MR 0227053 | Zbl 0153.02501

[3] G. Cattaneo G. Marino: Completeness of inner product spaces with respect to splitting subspaces. Letters in Math. Physics 11 (1986) 15-20. DOI 10.1007/BF00417459 | MR 0824671

[4] A. Dvurečenskij: Completeness of inner product spaces and quantum logic of splitting subspaces. Letters in Math. Physics 15 (1988) 231 - 235. DOI 10.1007/BF00398592 | MR 0948357

[5] A. Dvurečenskij: States on families of subspaces of pre-Hilbert spaces. Letters in Math. Physics 17 (1989) 19-24. DOI 10.1007/BF00420009 | MR 0990578

[6] P. D. Finch: Orthogonality relations and orthomodularity. Bull. Austral. Math. Soc. 2 (1970) 125-128. DOI 10.1017/S0004972700041678 | MR 0262122 | Zbl 0179.03401

[7] D. J. Foulis C. H. Randall: Lexicographic orthogonality. J. Combinatorial Theory Ser. A 11 (1971) 157-162. DOI 10.1016/0097-3165(71)90040-9 | MR 0280420

[8] R. Goldblatt: Orthomodularity is not elementary. Journal Symbolic Logic 49 (1984)401-404. MR 0745368 | Zbl 0593.03042

[9] H. Gross H. A. Keller: On the definition of Hilbert space. Manuscripta Math. 23 (1977) 67-90. DOI 10.1007/BF01168586 | MR 0482101

[10] S. P. Gudder: Projective representations of quantum logics. Internat. J. Theoret. Physics 3 (1970) 99-108. DOI 10.1007/BF02412750 | MR 0416297

[11] S. Gudder: Inner product spaces. Amer. Math. Monthly 81 (1974) 29-36. DOI 10.1080/00029890.1974.11993493 | MR 0331027 | Zbl 0279.46013

[12] S. Gudder: Correction to: „Inner product spaces". Amer. Math. Monthly 82 (1975) 251-252. MR 0420234

[13] S. Gudder S. Holland: Second correction to: „Inner product spaces". Amer. Math. Monthly 82 (1975) 818. DOI 10.1080/00029890.1975.11993943 | MR 0380374

[14] W. Guz: Filter theory and covering law. Ann. Inst. H. Poincarè Sec. A Phys. Thèor. 29 (1978) 357-378. MR 0525388 | Zbl 0398.03052

[15] J. Hamhalter P. Pták: A completeness criterion for inner product spaces. Bull. London Math. Soc. 19 (1987) 259-263. DOI 10.1112/blms/19.3.259 | MR 0879514

[16] L. Iturrioz: Orthomodular ordered sets and orthogonal closure spaces. Portugal. Math. 39 (1980) 477-488. MR 0776257

[17] G. Kalmbach: Orthomodular lattices. Academic Press, London, 1983. MR 0716496 | Zbl 0528.06012

[18] M. D. MacLaren: Atomic orthocomplemented lattices. Pacific J. Math. 14 (1964) 597-612. DOI 10.2140/pjm.1964.14.597 | MR 0163860 | Zbl 0122.02201

[19] F. Maeda S. Maeda: Theory of symmetric lattices. Springer-Verlag, Berlin 1970. MR 0282889

[20] C. Piron: Foundations of quantum physics. Benjamin, Reading, Massachusetts, 1976. MR 0673578 | Zbl 0333.46050

[21] R. Piziak: Orthomodular posets from sesquilinear forms. J. Austral. Math. Soc. 15 (1973) 265-269. DOI 10.1017/S1446788700013161 | MR 0325657 | Zbl 0271.15013

[22] S. Pulmannová: Superpositions of states and a representation theorem. Ann. Inst. H. Poincarè Sec. A Phys. Thèor. 32 (1980) 351-360. MR 0594634

[23] S. Pulmannová: Transition probability spaces. J. Math. Physics 27 (1986) 1791-1795. DOI 10.1063/1.527045 | MR 0844219

[24] V. S. Varadarajan: Geometry of quantum theory. 2nd ed., Springer-Verlag, New York, 1985. MR 0805158 | Zbl 0581.46061