Characterizing Mal’cev conditions

Taylor, Walter

doi:10.1007/bf02945141

Cited by 136 publications

(94 citation statements)

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“…As example applications of the viewpoint developed above, we derive two of W. Taylor's closure theorems [3]. We must first recall a definition ([2] p. 6): a set preserving functor F :^B l -> 93 2 between varieties is a pure forgetful functor if 23 2 is generated as a variety by the image of F, that is, 93 2 …”

Section: Closure Theoremsmentioning

confidence: 99%

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On Malcev conditions

Neumann

1974

J. Aust. Math. Soc.

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Section: Closure Theoremsmentioning

confidence: 99%

“…Though this viewpoint (so far) yields no new results, we feel it puts Walter Taylor's results [3] characterizing "Malcev definable classes of varieties" into a clearer perspective and is therefore worth mentioning. The author is grateful to R. Wille for pointing out W. Taylor's paper to him.…”

Section: Introductionmentioning

confidence: 99%

On Malcev conditions

Neumann

1974

J. Aust. Math. Soc.

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“…A brief discussion on the theory of multisorted varieties can be found in either [16] or [12]. Actually, the techniques developed in section 2 of this paper were inspired by the first part of Chapter 11 in [12], where the authors describe the categorical equivalence between the varieties of multisorted algebras and the varieties in 1-sorted algebraic signatures.…”

Section: Dejan Delićmentioning

confidence: 99%

A finitely axiomatizable undecidable equational theory with recursively solvable word problems

Delić

1999

Trans. Amer. Math. Soc.

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Abstract. In this paper we construct a finitely based variety, whose equational theory is undecidable, yet whose word problems are recursively solvable, which solves a problem stated by G. McNulty (1992). The construction produces a discriminator variety with the aforementioned properties starting from a class of structures in some multisorted language (which may include relations), axiomatized by a finite set of universal sentences in the given multisorted signature.This result also presents a common generalization of the earlier results obtained by B. Wells (1982) andA. Mekler, E. Nelson, andS. Shelah (1993).

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“…(In fact M^V) is simply the degree-1 part of the clone-see, for example, Taylor (1973), pp. 361-364-or the endomorphism monoid of the object 1 in the 'algebraic theory' of V-see, for example, (op.…”

Section: Varieties Of Varietiesmentioning

confidence: 99%

Mal'tsev conditions and spectra

Taylor

1980

J Aust Math Soc A

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Let J be a cofinite set of positive integers which contains 1. In (1973) I proved that the following condition on a variety (equational class) "f is Mal'tsev-definable: if 21 e y and 21 is finite, then 1211 eJ. This article contains some subsidiary results, concerned mainly with a more detailed description of these Mal'tsev conditions. Many of our results arose upon considering a recent article of W. D. Neumann (1978).To restate the above result in more detail, let us first recall that the spectrum of a variety "T is the set of finite cardinalities of algebras in V. Then that theorem asserts the existence, for each/, of a sequence

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Characterizing Mal’cev conditions

Cited by 136 publications

References 57 publications

On Malcev conditions

On Malcev conditions

A finitely axiomatizable undecidable equational theory with recursively solvable word problems

Mal'tsev conditions and spectra

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