Operations in polyadic algebras

Daigneault, Aubert

doi:10.1090/s0002-9947-1971-0285368-8

Cited by 8 publications

(3 citation statements)

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“…169-209, 251-257] and [30]. Regrettably, these constructions have turned out to be highly involved, in spite of efforts of several authors to simplify the initial approach (see, for example, [17]), and have not been used much even inside algebraic logic.…”

Section: Introductionmentioning

confidence: 99%

Freeoids: a semi-abstract view on endomorphism monoids of relatively free algebras

Cı̄rulis

2011

Algebra Univers.

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A freeoid over a (normally, infinite) set of variables X is defined to be a pair (W, E), where W is a superset of X, and E is a submonoid of W W containing just one extension of every mapping X → W . For instance, if W is a relatively free algebra over a set of free generators X, then the pair F (W) := (W, End (W)) is a freeoid. In the paper, the kernel equivalence and the range of the transformation F are characterized. Freeoids form a category; it is shown that the transformation F gives rise to a functor from the category of relatively free algebras to the category of freeoids which yields a concrete equivalence of the first category to a full subcategory of the second one. Also, the concept of a model of a freeoid is introduced; the variety generated by a free algebra W is shown to be concretely equivalent to the category of models of F (W). The sets X, W , and the algebras W may generally be many-sorted.

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Section: Introductionmentioning

confidence: 99%

Freeoids: a semi-abstract view on endomorphism monoids of relatively free algebras

Cı̄rulis

2011

Algebra Univers.

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confidence: 99%

Terms in cylindric algebras

Pinter¹

1973

Proc. Amer. Math. Soc.

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Abstract.A new algebraic treatment of terms within the framework of cylindric algebras.The theory of terms in locally finite polyadic algebras of infinite degree has been developed by Paul Halmos [2] and Aubert Daigneault [1]. In this paper we present a simple, new treatment of terms in dimension complemented cylindric algebras of infinite degree. By taking advantage of the presence of diagonal elements (which cannot be assumed to exist in arbitrary polyadic algebras), and by exploiting the well-known correspondence between operations and predicates which are single-valued in one of their variable places, we are able to introduce terms in a manner which is direct, well motivated and easy to use.

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“…The theory of terms in locally finite polyadic algebras of infinite degree has been developed by Paul Halmos [2] and Aubert Daigneault [1]. In this paper we present a simple, new treatment of terms in dimension complemented cylindric algebras of infinite degree.…”

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confidence: 99%