Orthomodular Posets Related to Z 2-Valued States
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We study orthocomplemented posets (certain quantum logics) that possess an abundance of Z 2-valued states. We first discuss their basic properties and, by means of examples, we illuminate intrinsic qualities of these orthocomplemented posets. We then address the problem of axiomatizability of our class of posets—a question that appears natural from the algebraic point of view. In the last section we show, as a main result, that supports of the posets endowed with symmetric difference constitute an important example of orthocomplemented posets under consideration. This result is obtained by a thorough analysis of certain types of ideals.
KeywordsOrthocomplemented poset Quantum logic Symmetric difference Boolean algebra Group-valued state