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 Ptak (1983), Navara (1989), Ovchinnikov (1999), Ptak (2000), Ptak and Pulmannova (1991), Prather (1980), Sherstnev (1968), Sultanbekov (1992), and Svozil (1998).
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