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On relative universality and Q-universality

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Abstract

Adams and Dziobiak proved that any finite-to-finite universal quasivariety must be Q-universal, and then asked whether a somewhat weaker hypothesis could lead to the same conclusion. We show that their original hypothesis cannot be weakened to its naturally extreme form.

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References

  1. Adams, M. E., and W. Dziobiak, ‘Lattices of quasivarieties of 3-element algebras’, J. of Algebra 166:181–210, 1994.

    Google Scholar 

  2. Adams, M. E., and W. Dziobiak, ‘Finite-to-finite universal quasivarieties are Q-universal’, Algebra Universalis 46:253–283, 2001.

    Google Scholar 

  3. Davey, B. A., ‘Subdirectly irreducible distributive double p-algebras’, Algebra Universalis 8:73–88, 1978.

    Google Scholar 

  4. Koubek, V., ‘Finite-to-finite universal varieties of distributive double p-algebras’, Comment. Math. Univ. Carolin. 31:67–83, 1990.

    Google Scholar 

  5. Koubek, V., and J. Sichler, ‘Universal finitely generated varieties of double p-algebras’, Cahiers Topologie Géom. Différentielle 35:139–164, 1994.

    Google Scholar 

  6. Koubek, V., and J. Sichler, ‘Equimorphy in varieties of distributive double p-algebras’, Czechoslovak Math. J. 48:473–544, 1998.

    Google Scholar 

  7. Priestley, H. A., ‘Representation of distributive lattices by means of ordered Stone spaces’, Bull. London Math. Soc. 2:186–190, 1970.

    Google Scholar 

  8. Priestley, H. A., ‘Ordered sets and duality for distributive lattices’, Ann. Discrete Math. 23:36–60, 1984.

    Google Scholar 

  9. Pultr, A., and V. Trnková, Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories, North Holland, 1980.

  10. Sapir, M. V., ‘The lattice of quasivarieties of semigroups’, Algebra Universalis 21:172–180, 1985.

    Google Scholar 

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Authors and Affiliations

  1. Department of Theoretical Computer Science and Institute of Theoretical Computer Science Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    V. Koubek

  2. Department of Mathematics, University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada

    J. Sichler

Authors
  1. V. Koubek
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  2. J. Sichler
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Additional information

To Professor Aleš Pultr on his 65th birthday

The authors gratefully acknowledge the support of the NSERC of Canada, of the project LN00A056 of the Czech Ministry of Education, and also of the Grant Agency of Czech Republic under the grant 201/02/0148.

Special issue of Studia Logica: “Algebraic Theory of Quasivarieties” Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko

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Koubek, V., Sichler, J. On relative universality and Q-universality. Stud Logica 78, 279–291 (2004). https://doi.org/10.1007/s11225-005-0291-5

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  • DOI: https://doi.org/10.1007/s11225-005-0291-5

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