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Finite quasivarieties and self-referential conditions

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Abstract

In this paper, we concentrate on finite quasivarieties (i.e. classes of finite algebras defined by quasi-identities). We present a motivation for studying finite quasivarieties. We introduce a new type of conditions that is well suited for defining finite quasivarieties and compare these new conditions with quasi-identities.

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References

  1. Almeida J., Finite semigroups and universal algebra, World Scientific, 1994.

  2. Almeida J., ‘On the membership problem for pseudovarieties of commutative semigroups’, Semigroup Forum 42 (1991), 47–51.

    Google Scholar 

  3. Almeida J., and M.V. Volkov, ‘Profinite methods in finite semigroup theory’, in S.S. Goncharov, (ed.), Proceedings of International Conferences on Mathematical Logic, Novosibirsk State University, Novosibirsk, 2002, pp. 3–28.

    Google Scholar 

  4. Ash, C.J., ‘Pseudovarieties, generalized varieties, and similarly described classes’, Journal of Algebra 92 (1985), 104–115.

    Google Scholar 

  5. Bird, R., and O. de Moor, Algebra of Programming, Prentice Hall, 1997.

  6. Clifford, A.H., and G.B. Preston, The algebraic theory of semigroups, vol. 1 and 2, Mathematical surveys of the American Mathematical Society, 1961 and 1967.

  7. Cohn, P. M., Universal algebra, D. Reidel Publishing Company, 1981.

  8. Bloom, S. and Z. Ésik, Iteration Theories. The Equational Logic of Iterative Processes, Springer-Verlag, 1993.

  9. Gorbunov, V. A., ‘Structure of lattices of varieties and lattices of quasivarieties: their similarity and difference. I’, Algebra Logika 34 (1995), 142–168 [English translation: Algebra Logic 34 (1995), 73–86].

    Google Scholar 

  10. Gorbunov, V. A., Algebraic Theory of Quasivarieties, Plenum Publishing Co., 1998.

  11. Hall, T. E., and S. I. Kublanovskii, S. Margolis, M. V. Sapir, P. G. Trotter, ‘Algorithmic problems for finite groups and finite 0-simple semigroups’, Journal of Pure and Applied Algebra 119 (1997), 75–96.

    Google Scholar 

  12. Repnitskii, V. B., and A. S. Vernitski, ‘Semigroups of order-preserving mappings’, Communications in Algebra 28 (2000), 3635–3641.

    Google Scholar 

  13. Trahtman A. N., ‘Algorithms verifying local threshold and piecewise testability of semigroups and solving Almeida problem’, RIMS Kokyuroku Proceedings of Kyoto University 1222 (2001), 145–151.

    Google Scholar 

  14. Vernitski, A.S., The semigroups of order-preserving mappings: quest for quasi-identities, in J. M. Howie and N. Ruškuc, (ed.), Semigroups and Applications 1998.

  15. Vernitski, A. S., Classes of semigroups closed under taking subsemigroups and finite direct products (PhD thesis), Department of Mathematics, University of Essex, Colchester, UK, 1998.

    Google Scholar 

  16. Vernitski, A. S., ‘Studying semigroups of mappings using quasi-identities’, Semigroup Forum 63 (2001), 387–395.

    Google Scholar 

  17. Volkov, M. V., ‘On a class of semigroup pseudovarieties without finite pseudoidentity basis’, International Journal of Algebra and Computation 5 (1995), 127–135.

    Google Scholar 

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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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Vernitski, A. Finite quasivarieties and self-referential conditions. Stud Logica 78, 337–348 (2004). https://doi.org/10.1007/s11225-005-7348-3

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  • DOI: https://doi.org/10.1007/s11225-005-7348-3

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