Mayet, René Equational bases for some varieties of orthomodular lattices related to states. (English) Zbl 0618.06003 Algebra Univers. 23, 167-195 (1986). In his former paper [Algebra Univers. 20, 368-396 (1985; Zbl 0581.06006)] the author studied varieties of orthomodular lattices which were determined by conditions on states. In this paper he considers equations valid in those varieties and shows that many of the varieties admit a recursive equational base. He also develops a constructive procedure for obtaining an equation valid in a given finite orthomodular lattice outside a variety. Reviewer: P.Pták Cited in 8 Documents MSC: 06C15 Complemented lattices, orthocomplemented lattices and posets 03C05 Equational classes, universal algebra in model theory 46L30 States of selfadjoint operator algebras 06B20 Varieties of lattices 08B05 Equational logic, Mal’tsev conditions 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) Keywords:varieties of orthomodular lattices; states; equations; recursive equational base; finite orthomodular lattice Citations:Zbl 0581.06006 PDFBibTeX XMLCite \textit{R. Mayet}, Algebra Univers. 23, 167--195 (1986; Zbl 0618.06003) Full Text: DOI References: [1] E.Beltrametti and G.Cassinelli,The logic of Quantum Mechanics, Addison-Wesley Pub. Comp. (1981). · Zbl 0491.03023 [2] C. C.Chang and H. J.Keistler,Model Theory, North-Holland Pub. Comp. (1973). [3] R. Godowski,Varieties of orthomodular lattices with a strongly full set of states, Demonstratio Mathematica XIV, No.3 (1981), 725-732. · Zbl 0483.06007 [4] R. Godowski,States on orthomodular lattices, Demonstratio Mathematica XV, No.3 (1982), 817-822. · Zbl 0522.06010 [5] R. Godowski andR. J. Greechie,Some equations related to states on orthomodular lattices, Demonstratio Mathematica XVII, No. 1 (1984), 241-250. · Zbl 0553.06013 [6] R. J. Greechie,Orthomodular lattices admitting no states, Journal of Combinatorial Theory,10 (1971), 119-132. · Zbl 0219.06007 · doi:10.1016/0097-3165(71)90015-X [7] G. Kalmbach,Orthomodular Lattices, Academic Press, New York (1983). [8] R. Mayet,Varieties of orthomodular lattices related to states, Algebra Universalis,20, 3 (1985), 368-396. · Zbl 0581.06006 · doi:10.1007/BF01195144 [9] M. Rabin,Decidable theories, in Handbook of Mathematical logic, ed. J. Barwise, North-Holland, New York, (1977). [10] A.Robinson,Non-standard Analysis, North-Holland Pub. Comp. (1966). · Zbl 0151.00803 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.