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On centers and state spaces of logics. (English) Zbl 0544.03034
Let P, Q be $$\sigma$$-orthoposets $$(=$$ quantum logics). The question is if there is a $$\sigma$$-orthoposet L such that the center of L coincides with the center of P and the state space of L coincides with the state space of Q. The paper brings an affirmative answer to this question for certain classes of $$\sigma$$-orthoposets.

##### MSC:
 03G12 Quantum logic 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) 06C20 Complemented modular lattices, continuous geometries
##### Keywords:
orthomodular poset; center; state space