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The Varieties Defined by P-compatible Identities of Modular Ortholattices

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Abstract

In the present paper we give syntactical and semantical characterization of the class of algebras defined by P-compatible identities of modular ortholattices. We also describe the lattice of some subvarieties of the variety MOL Ex defined by so called externally compatible identities of modular ortholattices.

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References

  1. Birkhoff G., J. Von Neumann: ‘The Logic of Quantum Mechanics’. The Annals of Mathematics 37(4), 823–843 (1936)

    Article  Google Scholar 

  2. Burris S., H.P. Sankappanavar: A Course in Universal Algebra. Springer-Verlag, New York (1981)

    Google Scholar 

  3. Chromik W.: ‘Externally compatible identities of algebras’. Demonstratio Mathematica 23, 345–355 (1990)

    Google Scholar 

  4. Gajewska-Kurdziel K.: ‘On the lattice of some varieties defined by P-compatible identities’. Zeszyty Naukowe Uniwersytetu Opolskiego, Matematyka 29, 45–47 (1995)

    Google Scholar 

  5. Hałkowska K.: ‘Equational theories of varieties defined by P-compatible identities of Boole’an algebras’. Beiträzur Algebra und Geometrie 33, 103–108 (1992)

    Google Scholar 

  6. Hałkowska K.: ‘Lattice of equational theories of P-compatible varieties’. In: Orłowska, E. (eds) Logic at Work Essays dedicated to the memory of Helena Rasiowa, pp. 587–595. Springer Heidelberg, New York (1998)

    Google Scholar 

  7. Malinowski J.: ‘Quasivarieties of modular ortholattices’. Bulletin of the Section of Logic. 20(3–4), 138–142 (1991)

    Google Scholar 

  8. Mel’nik, I. I., ‘Nilpotent shifts of varieties’, Mat. Zametki 14 (5), 1973 [in Russian]. English translation: Math. Notes 14: 962–966, 1973.

  9. Miyazaki Y.: ‘Some Properties of Orthologics’. Studia Logica. 80, 75–93 (2005)

    Article  Google Scholar 

  10. Pigozzi D.: ‘On some operations on classes of algebras’. Algebra Universalis. 2(1), 346–353 (1972)

    Article  Google Scholar 

  11. Płonka J.: ‘On the subdirect product of some equational classes of algebras’. Math. Nachr. 63, 303–305 (1974)

    Google Scholar 

  12. Płonka J.: ‘P-compatible identities and their applications to classical algebras’. Math. Slovaca. 40(1), 21–30 (1990)

    Google Scholar 

  13. Tarski A.: ‘A remark on functionally free algebras’. The Annals of Mathematics. 47(1), 163–166 (1946)

    Article  Google Scholar 

  14. Tarski A., ‘Equational logic and equational theories of algebras’, in H.A. Schmidt, K. Schüand H. J. Thiele, (eds.), Contributions to Mathematical Logic, Nort Holland Publ. Co., Amsterdam, pp. 275–288.

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  1. Department of Logic, Nicolaus Copernicus University of Toruń, ul. Asnyka 2, 87-100, Toruń, Poland

    Krystyna Mruczek-Nasieniewska

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  1. Krystyna Mruczek-Nasieniewska
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Correspondence to Krystyna Mruczek-Nasieniewska.

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Mruczek-Nasieniewska, K. The Varieties Defined by P-compatible Identities of Modular Ortholattices. Stud Logica 95, 21–35 (2010). https://doi.org/10.1007/s11225-010-9255-5

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