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- Title
Extending States on Finite Concrete Logics.
- Authors
Svozil, Karl; de Simone, Anna; Navara, Mirko; Pták, Pavel
- Abstract
In this note we collect several observations on state extensions. They may be instrumental to anyone who pursues the theory of quantum logics. In particular, we find out when extensions (resp. signed extensions) exist in the “concrete” concrete logic of all even-element subsets of an even-element set (Theorems 2.3 and 2.9). We also mildly add to the study of difference-closed logics as initiated in Ovchinnikov (1999) by finding an extension theorem for subadditive states. Our results supplement the research carried on in De Simone (2000), Gudder (1979), Gudder and Marchand (1980), Navara and Pták (1983), Navara (1989), Ovchinnikov (1999), Pták (2000), Pták and Pulmannová (1991), Sherstnev (1968), Sultanbekov (1992), and Svozil (1998).
- Subjects
QUANTUM logic; MATHEMATICAL physics; QUANTUM theory; MATHEMATICAL logic; PHYSICS; MECHANICS (Physics)
- Publication
International Journal of Theoretical Physics, 2005, Vol 44, Issue 7, p1087
- ISSN
0020-7748
- Publication type
Article
- DOI
10.1007/s10773-005-7083-6