The Birkhoff theorem for finite algebras. (English) Zbl 0484.08007


08C15 Quasivarieties
08C10 Axiomatic model classes
08A02 Relational systems, laws of composition


Zbl 0351.20035
Full Text: DOI


[1] J. T. Baldwin andJ. Berman,Varieties and finite closure conditions, Coll. Math.35 (1976), 15–20. · Zbl 0328.08004
[2] B. Banaschewski,On equationally compact extensions of algebras, Alg. Univ.4 (1974), 20–35. · Zbl 0314.08005
[3] B. Banaschewski,Profinite universal algebras, in: Proceedings of the Third Prague Topological Symposium, Academia Prague 1971, 51–62.
[4] G. Birkhoff,On the structure of abstract algebras, Proc. Cambridge Phil. Soc.31 (1935), 433–454. · JFM 61.1026.07
[5] S. Bulman-Fleming,Congruence topologies on universal algebras, Math. Z.119 (1971), 287–289. · Zbl 0205.31903
[6] P. M. Cohn,Universal algebra, Harper and Row, New York, Evanston and London 1965.
[7] S. Eilenberg, Automata, languages and machines, Volume B, Academic Press, New York, San Francisco, London 1976. · Zbl 0359.94067
[8] S. Eilenberg andM. P. Schützenberger,On pseudovarieties, Advances in Math.19 (1976), 413–418. · Zbl 0351.20035
[9] T. Evans,Approximating algebras by finite algebras, Seminaire Mathématique Superieures, L’Université de Montréal 1971.
[10] P. Goralčík andV. Koubek,Pseudovarieties and pseudotheories, to appear in Proceedings of Colloquium on Finite Algebra and Multiple Valued Logic, Szeged 1979.
[11] G. Grätzer,Universal algebra, D. van Nostrand, Princeton 1968.
[12] M. Hull,A topology for free groups and related groups, Ann. of Math. (2)52 (1950), 127–139. · Zbl 0045.31204
[13] J. F. Kennison andD. Gildenhuys,Equational completions, model induced triples and pro-objects, J. Pure Appl. Algebra1 (1971), 317–346. · Zbl 0234.18006
[14] F. W. Lawvere, Functorial semantics of algebraic theories, dissertation, Columbia University 1963. · Zbl 0119.25901
[15] F. W. Lawvere, Some algebraic problems in the context of functorial semantics of algebraic theories, in: Lecture Notes in Mathematics 61, Springer-Verlag 1968, 41–61. · Zbl 0204.33802
[16] V. Müller: Algebras and R-algebras, thesis, Charles University Prague 1973.
[17] J. Mycielski andW. Taylor,A compactification of the algebra of terms, Alg. Univ.6 (1976), 161–163. · Zbl 0358.08001
[18] J. Rosický andL. Polák,Definability on finite algebras, to appear in Proceedings of Colloquium on Finite Algebra and Multiple Valued Logic, Szeged 1979.
[19] W. Taylor,Some constructions of compact algebras, Ann. Math. Logic3 (1971), 395–435. · Zbl 0239.08003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.