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Categorical quasivarieties via Morita equivalence

Published online by Cambridge University Press:  12 March 2014

Keith A. Kearnes
Keith A. Kearnes*
Affiliation:
Department of Mathematics, University of Louisville, Louisville, KY 40292, USA, E-mail: [email protected]
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Abstract

We give a new proof of the classification of ℵ0-categorical quasivarieties by using Morita equivalence to reduce to term minimal quasivarieties.

Keywords

abelian algebracategorical quasivarietyMorita equivalencepermutational algebraterm minimal algebra
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 2 , June 2000 , pp. 839 - 856
Copyright
Copyright © Association for Symbolic Logic 2000

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References

REFERENCES

[1]Baldwin, J. T. and Lachlan, A. H., On universal Horn classes categorical in some infinite power, Algebra Universalis, vol. 3 (1973), pp. 98–111.CrossRefGoogle Scholar
[2]Baldwin, J. T. and McKenzie, R., Counting models in universal Horn classes, Algebra Universalis, vol. 15 (1982), pp. 359–384.CrossRefGoogle Scholar
[3]Givant, S., Universal Horn classes categorical or free in power, Annals of Mathematical Logic, vol. 15 (1978), pp. 1–53.CrossRefGoogle Scholar
[4]Givant, S., A representation theorem for universal Horn classes categorical in power, Annals of Mathematical Logic, vol. 17 (1979), pp. 91–116.CrossRefGoogle Scholar
[5]Hobby, D. and McKenzie, R., The structure of finite algebras, Contemporary Mathematics, vol. 76, American Mathematical Society, 1988.CrossRefGoogle Scholar
[6]Hodges, W., Model theory, Encyclopedia of Mathematics and its Applications, vol. 42, Cambridge University Press, 1993.CrossRefGoogle Scholar
[7]Kearnes, K. A., Idempotent simple algebras, Logic and algebra, proceedings of the Magari memorial conference, Siena 1994, Marcel Dekker, New York.Google Scholar
[8]Kearnes, K. A., Local methods in universal algebra, preprint, 1996.Google Scholar
[9]Kearnes, K. A. and Szendrei, Á., A characterization of minimal locally finite varieties, Transactions of the American Mathematical Society, vol. 349 (1997), pp. 1749–1768.CrossRefGoogle Scholar
[10]Kiss, E. W., An easy way to minimal algebras, International Journal Algebra Comput., vol. 7 (1997), pp. 55–75.CrossRefGoogle Scholar
[11]McKenzie, R., Categorical quasivarieties revisited, Algebra Universalis, vol. 19 (1984), pp. 273–303.CrossRefGoogle Scholar
[12]McKenzie, R., An algebraic version of categorical equivalence for varieties and more general algebraic categories, Logic and algebra (Pontignano, 1994), Lecture Notes in Pure and Applied Mathematics, vol. 180, Marcel Dekker, New York, 1996, pp. 211–243.Google Scholar
[13]Pálfy, P. P., Unary polynomials in algebras, I, Algebra Universalis, vol. 18 (1984), pp. 262–273.CrossRefGoogle Scholar
[14]Pálfy, P. P. and Szendrei, Á., Unary polynomials in algebras, II, Contributions to general algebra, Verlag Hölder-Pichler-Tempsky, Wien, Verlag Teubner, Stuttgart, 1983, pp. 273–290.Google Scholar
[15]Palyutin, E. A., Categorical quasivarieties of arbitrary signature, Siberian Mathematical Journal, vol. 14 (1974), pp. 904–916, Russian original in Siberian Mathematical Journal, vol. 14 (1973), pp. 1285–1303.CrossRefGoogle Scholar
[16]Palyutin, E. A., The description of categorical quasivarieties, Algebra and Logic, vol. 14 (1976), pp. 86–111, Russian original in Algebra i Logika, 14 (1975), pp. 263–303.CrossRefGoogle Scholar
[17]Szendrei, Á., >Clones in universal algebra, Séminaire de Mathétiques Superieures, vol. 99, Les Presses de l'Université de Montréal, Montréal, 1986.Google Scholar
[18]Szendrei, Á., Idempotent algebras with restrictions on subalgebras, Acta Sci Math., vol. 51 (1987), pp. 251–268.Google Scholar
[19]Szendrei, Á., Simple surjective algebras having no proper subalgebras, Journal of the Australian Mathematical Society, vol. 48 (1990), pp. 434–454.CrossRefGoogle Scholar
[20]Szendrei, Á., Term minimal algebras, Algebra Universalis, vol. 32 (1994), pp. 439–477.CrossRefGoogle Scholar