Countable Jauch-Piron logics
The author shows that every orthomodular lattice with a finite- dimensional space of bounded finitely additive signed measures has a countable model (i.e., a countable subortholattice such that every finitely additive state on it can be uniquely extended to a finitely additive state on the given ortholattice). As a consequence (using the Gleason theorem) he gives examples of countable unital Jauch-Piron orthomodular lattices that are not Boolean (models of lattices of all subspaces of \(R^ n\), \(n>3\)). This remarkable result completes the result of \textit{V. Rogalewicz} [Int. J. Theor. Phys. 30, No. 4, 437-445 (1991; Zbl 0728.03034)], who proved that the number of blocks of a unital Jauch-Piron orthomodular poset is finite if and only if it equals 1. In the appendix an older result concerning the characterization of orthomodular posets by means of two-element and three-element partitions of unity is presented.
scientific article; zbMATH DE number 465575