caa a22 4500 463197070 CHVBK 20180406164925.0 cr unu---uuuuu 170326e20070801xx s 000 0 eng 10.1007/s10773-006-9298-6 doi (NATIONALLICENCE)springer-10.1007/s10773-006-9298-6 Extending States on Finite Concrete Logics [Elektronische Daten] [Anna De Simone, Mirko Navara, Pavel Pták] 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). Springer Science+Business Media, LLC, 2007 (concrete) quantum logic nationallicence state nationallicence extension nationallicence De Simone Anna Dipartimento di Matematica e Statistica, Università Federico II di Napoli, Complesso Monte S. Angelo, Via Cintia, 80126, Napoli, Italy aut Navara Mirko Center for Machine Perception, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University, Technická 2, 166 27, Prague, Czech Republic aut Pták Pavel Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University, Technická 2, 166 27, Prague, Czech Republic aut International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/8(2007-08-01), 2046-2052 0020-7748 46:8<2046 2007 46 10773 https://doi.org/10.1007/s10773-006-9298-6 text/html Onlinezugriff via DOI 1 other jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-006-9298-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- De Simone Anna Dipartimento di Matematica e Statistica, Università Federico II di Napoli, Complesso Monte S. Angelo, Via Cintia, 80126, Napoli, Italy aut NATIONALLICENCE 700 1- Navara Mirko Center for Machine Perception, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University, Technická 2, 166 27, Prague, Czech Republic aut NATIONALLICENCE 700 1- Pták Pavel Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University, Technická 2, 166 27, Prague, Czech Republic aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/8(2007-08-01), 2046-2052 0020-7748 46:8<2046 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer