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Spaces of Abstract Events

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Faculty of Science, Department of Algebra and Geometry, Palacký University Olomouc, 17. listopadu 12, 77146, Olomouc, Czech Republic

    Ivan Chajda

  2. Faculty of Mathematics and Geoinformation, Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8–10, 1040, Vienna, Austria

    Helmut Länger

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  1. Ivan Chajda
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  2. Helmut Länger
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Correspondence to Helmut Länger.

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Chajda, I., Länger, H. Spaces of Abstract Events. Int J Theor Phys 52, 1818–1824 (2013). https://doi.org/10.1007/s10773-012-1275-7

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  • DOI: https://doi.org/10.1007/s10773-012-1275-7

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