International Journal of Theoretical Physics

, Volume 53, Issue 10, pp 3323–3332 | Cite as

Orthomodular Posets Related to Z 2-Valued States

  • Milan Matoušek
  • Pavel Pták


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.


Orthocomplemented poset Quantum logic Symmetric difference Boolean algebra Group-valued state 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Ruská 22Prague 10Czech Republic
  2. 2.Department of Mathematics, Faculty of Electrical Eng.Czech Technical UniversityPrague 6Czech Republic

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