Axiomatizability and completeness of some classes of s-polygons

Stepanova, A. A.

doi:10.1007/bf01980252

Cited by 11 publications

(11 citation statements)

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“…Those monoids for which P is axiomatisable were determined by the fourth author in [22], using preliminary results of the first author from [10]. In fact, P is axiomatisable if and only if SF is axiomatisable and P = SF .…”

Section: Axiomatisability Of Pmentioning

confidence: 99%

“…The question of axiomatisability of F r was solved in some special cases by the fourth author in [22], and most recently by the first author as below.…”

Section: Axiomatisability Of F Rmentioning

confidence: 99%

“…We devote Sections 5 to 9 to characterising those monoids S such that the classes of weakly flat, flat, strongly flat, projective and free S-acts are axiomatisable. The material for Sections 5 to 8 is taken from the papers [10] and [2] of the first author and Bulman-Fleming, and the paper [22] of the fourth author. Section 9 contains a new result of the first author characterising those monoids such that the class of free left S-acts is axiomatisable, and some specialisations taken from [22].…”

Section: Introductionmentioning

confidence: 99%

“…[22] Let S be a monoid such that every ultrapower of S as a left S-act is projective. Then S satisfies (CFRS).…”

mentioning

confidence: 99%

“…[22] Let S be an inverse monoid. Then F r is an axiomatisable class if and only if P is axiomatisable and H 1 has finite right index in S.…”

mentioning

confidence: 99%

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Model-theoretic properties of free, projective, and flat S-acts

et al. 2009

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This is the second in a series of articles surveying the body of work on the model theory of S-acts over a monoid S. The first concentrated on the theory of regular S-acts. Here we review the material on model-theoretic properties of free, projective and (strongly, weakly) flat S-acts. We consider questions of axiomatisability, completeness, model completeness and stability for these classes. Most but not all of the results have already appeared; we remark that the description of those monoids S such that the class of free left S-acts is axiomatisable, is new.

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Section: Axiomatisability Of Pmentioning

confidence: 99%

“…The question of axiomatisability of F r was solved in some special cases by the fourth author in [22], and most recently by the first author as below.…”

Section: Axiomatisability Of F Rmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…[22] Let S be a monoid such that every ultrapower of S as a left S-act is projective. Then S satisfies (CFRS).…”

mentioning

confidence: 99%

“…[22] Let S be an inverse monoid. Then F r is an axiomatisable class if and only if P is axiomatisable and H 1 has finite right index in S.…”

mentioning

confidence: 99%

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Model-theoretic properties of free, projective, and flat S-acts

et al. 2009

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Axiomatisability problems for S-posets

Gould

Shaheen

2010

Semigroup Forum

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Let C be a class of algebras of a given fixed type τ . Associated with the type is a first order language L τ . One can then ask the question, when is the class C axiomatisable by sentences of L τ ? In this paper we will be considering axiomatisability problems for classes of left S-posets over a pomonoid S (that is, a monoid S equipped with a partial order compatible with the binary operation). We aim to determine the pomonoids S such that certain categorically defined classes are axiomatisable. The classes we consider are the free S-posets, the projective S-posets and classes arising from flatness properties. Some of these cases have been studied in a recent article by Pervukhin and Stepanova. We present some general strategies to determine axiomatisability, from which their results for the classes of weakly po-flat and po-flat S-posets will follow. We also consider a number of classes not previously examined.

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Axiomatisability problems for S-acts, revisited

Shaheen

2012

Semigroup Forum

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Axiomatizability and completeness of some classes of s-polygons

Cited by 11 publications

References 4 publications

Model-theoretic properties of free, projective, and flat S-acts

Model-theoretic properties of free, projective, and flat S-acts

Axiomatisability problems for S-posets

Axiomatisability problems for S-acts, revisited

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