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Orthoalgebras as Pastings of Boolean Algebras

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Abstract

We correct a mistake in the description of orthoalgebras as pastings of Boolean algebras. We present a corrected structural theorem.

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Notes

  1. This definition of a suborthoalgebra follows [14]

  2. For the definitions and basic properties of orthomodular posets and lattices, we refer to [1, 5, 9, 13].

References

  1. Beran, L.: Orthomodular Lattices. Algebraic Approach. Academia, Praha (1984)

    MATH  Google Scholar 

  2. Chovanec, F.: Graphic representation of MV-algebra pastings. Math. Slovaca 63, 349–380 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chovanec, F.: Difference Posets and Their Graphical Representation (in Slovak). Military Academy, Liptovský Mikuláš, Slovakia (2013)

    Google Scholar 

  4. Dichtl, M.: Astroids and pastings. Algebra Universalis 18, 380–385 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  5. Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures. Kluwer/Dordrecht & Ister/Bratislava (2000)

  6. Golfin, A.: Representations and Products of Lattices. PhD Thesis, University of Massachusetts, Amherst, MA (1987)

  7. Greechie, R.J.: Orthomodular lattices admitting no states. J. Combin. Theory Ser. A 10, 119–132 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hamhalter, J., Navara, M., Pták, P.: States on orthoalgebras. Internat. J. Theoret. Phys. 34(8), 1439–1465 (1995)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  9. Kalmbach, G.: Orthomodular Lattices. Academic Press, London (1983)

    MATH  Google Scholar 

  10. Navara, M., Rogalewicz, V.: The pasting constructions for orthomodular posets. Math. Nachrichten. 154, 157–168 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  11. Navara, M.: State spaces of orthomodular structures. Rend. Istit. Mat. Univ. Trieste 31 (2000), Suppl. 1, 143–201

  12. Navara, M.: Constructions of quantum structures. In: Gabbay, D., Lehmann, D., Engesser, K. (eds.) Handbook of Quantum Logic, Vol. 1, Elsevier, pp 335–366 (2007)

    Chapter  Google Scholar 

  13. Pták, P., Pulmannová, S.: Orthomodular Structures as Quantum Logics. Kluwer Academic Publishers, Dordrecht/Boston/London (1991)

    MATH  Google Scholar 

  14. Riečanová, Z.: Subalgebras, intervals and central elements of generalized effect algebras. Internat. J. Theoret. Phys. 38, 3209–3220 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  15. Shultz, F.W.: A characterization of state spaces of orthomodular lattices. J. Comb. Theory A 17, 317–328 (1974)

    Article  MathSciNet  Google Scholar 

  16. Wright, R.: The structure of projection-valued states: A generalization of Wigner’s theorem. Internat. J. Theoret. Phys. 16, 567–573 (1977)

    Article  ADS  MATH  MathSciNet  Google Scholar 

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Acknowledgments

The author was supported by the Ministry of Education of the Czech Republic under Project RVO13000. Special thanks go to Bruce Legan who recognized a mistake in previous work.

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Authors and Affiliations

  1. Center for Machine Perception, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 166 27, Prague, Czech Republic

    Mirko Navara

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  1. Mirko Navara
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Correspondence to Mirko Navara.

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Navara, M. Orthoalgebras as Pastings of Boolean Algebras. Int J Theor Phys 56, 4126–4132 (2017). https://doi.org/10.1007/s10773-017-3479-3

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  • DOI: https://doi.org/10.1007/s10773-017-3479-3

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