Spaces of Abstract Events
We generalize the concept of a space of numerical events in such a way that this generalization corresponds to arbitrary orthomodular posets whereas spaces of numerical events correspond to orthomodular posets having a full set of states. Moreover, we show that there is a natural one-to-one correspondence between orthomodular posets and certain posets with sectionally antitone involutions. Finally, we characterize orthomodular lattices among orthomodular posets.
KeywordsNumerical event Abstract event Orthomodular poset Effect algebra State Full set of states Antitone involution Sectionally antitone involutions Orthomodular lattice
Support of the research of both authors by ÖAD, Cooperation between Austria and Czech Republic in Science and Technology, grant No. CZ 01/2011, and of the first author by the Project CZ.1.07/2.3.00/20.0051 Algebraic Methods of Quantum Logics is gratefully acknowledged.
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