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A study of independence in a set with orthogonality. (English) Zbl 0629.06009
The author studies three kinds of n-independence in a set \(\Omega\) with orthogonality, interrelations between them and maximal n-independent subsets of \(\Omega\). The “independent” concepts started from J. von Neumann’s 1930-1940 work on continuous geometries and have been studied in 1964-1982, as abstract orthogonality-versions, in papers by U. Bosch, D. Foulis, R. Goldblatt, L. Iturrioz, M. D. MacLaren, M. Szymanska.
Reviewer: G.Kalmbach

MSC:
06C15 Complemented lattices, orthocomplemented lattices and posets
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
06C20 Complemented modular lattices, continuous geometries
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