A note on Jauch-Piron states
A logic (orthomodular poset) L is called Jauch-Piron if for each state (finitely additive probability measure) s on L and each a, \(b\in L\) the equality \(s(a)=s(b)-1\) implies the existence of \(c\in L\) such that \(c\leq a\), \(c\leq b\), \(s(c)=1\). The author investigates the size of the class of Jauch-Piron logics. Besides general logics he studies these questions for hilbertian and set-representable \((=concrete)\) logics. He compares his results with those obtained for \(\sigma\)-additive states by \textit{L. Bunce}, \textit{M. Navara}, \textit{P. Pták} and \textit{J. D. M. Wright} [Quart. J. Math., Oxford II. Ser. 36, 261-271 (1985; Zbl 0585.03038)].
scientific article; zbMATH DE number 4014712
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