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On the definability of \(P_ S(A)\). (English) Zbl 0618.08005

A sufficient condition for the class, \(P_ s(A)\), of subdirect powers of a finite algebra A to be elementary was given by G. Grätzer [Acta Sci. Math. 25, 160-168 (1964; Zbl 0192.096)]. In this paper an algebraic necessary and sufficient condition for \(P_ s(A)\) to be elementary is provided, and also a syntactic sufficient condition which is weaker than Grätzer’s. (The conditions are too technical to give here.) The paper concludes by mentioning three interesting open questions.
Reviewer: S.Oates-Williams

MSC:

08C10 Axiomatic model classes
03C60 Model-theoretic algebra

Citations:

Zbl 0192.096
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References:

[1] G. Gr?tzer,On the class of subdirect powers of a finite algebra, Acta. Sci. Math.,25 (1964), 160-168. · Zbl 0192.09601
[2] G.Gr?tzer,Universal Algebra, Springer-Verlag, 1979.
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