NDLI: Extending States on Finite Concrete Logics

Content Provider	Paperity
Author	Simone, Anna De 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 (Th. 2.3 and Th. 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 suplement 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), Prather (1980), Sherstnev (1968), Sultanbekov (1992), and Svozil (1998).
Starting Page	2046
Ending Page	2052
File Format	HTM / HTML
ISSN	00207748
DOI	10.1007/s10773-006-9298-6
Issue Number	8
Journal	International Journal of Theoretical Physics
Volume Number	46
e-ISSN	15729575
Language	English
Publisher	Springer US
Publisher Date	2007-08-23
Access Restriction	Open
Subject Keyword	Extension (concrete) quantum logic State
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Mathematics

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Extending States on Finite Concrete Logics