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. 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 previously carried on by De Simone (2000), Gudder (1979), Gudder and Marchand (1980), Navara and Pt´ak (1983), Navara (1989), Ovchinnikov (1999), Ptak (2000), Ptak and Pulmannova (1991), Prather (1980), Sherstnev (1968), Sultanbekov (1992), and Svozil (1998).
Extending states on finite concrete logics / DE SIMONE, Anna; Navara, M; Ptak, P.. - In: INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS. - ISSN 0020-7748. - STAMPA. - 46:8(2007), pp. 2046-2052.
Extending states on finite concrete logics
DE SIMONE, ANNA;
2007
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. 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 previously carried on by De Simone (2000), Gudder (1979), Gudder and Marchand (1980), Navara and Pt´ak (1983), Navara (1989), Ovchinnikov (1999), Ptak (2000), Ptak and Pulmannova (1991), Prather (1980), Sherstnev (1968), Sultanbekov (1992), and Svozil (1998).File | Dimensione | Formato | |
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