PREPRINT SERIES 2010 / 2011 NO : 8 TITLE : ‘ AXIOMATISABILITY PROBLEMS FOR S - POSETS ’ AUTHOR ( S ) : Dr Victoria Gould
نویسندگان
چکیده
Let C be a class of ordered algebras of a given fixed type τ . Associated with the type is a first order language Lτ , which must also contain a binary predicate to be interpreted by the ordering in members of C. One can then ask the question, when is the class C axiomatisable by sentences of Lτ? 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.
منابع مشابه
Axiomatisability Problems for S-posets
Let C be a class of ordered algebras of a given fixed type τ . Associated with the type is a first order language Lτ , which must also contain a binary predicate to be interpreted by the ordering in members of C. One can then ask the question, when is the class C axiomatisable by sentences of Lτ? In this paper we will be considering axiomatisability problems for classes of left S-posets over a ...
متن کاملAxiomatisability Problems for S-acts, Revisited
This paper discusses necessary and sufficient conditions on a monoid S, such that a class D of left S-acts is first order axiomatisable. Such questions have previousely been considered by Bulman-Fleming, Gould, Stepanova and others. Let C be a class of embeddings of right S-acts. A left S-act B is C-flat if tensoring with any B ∈ D preserves the embeddings in C. We find one or two (depending on...
متن کاملAxiomatisability of free, projective and flat S-acts
We survey the known results characterising those monoids S such that the classes of free, projective or (weakly, strongly) flat S-acts are first order axiomatisable. The conditions on the monoid S that arise are finitary, and intricately related. We examine their inter-connections and illustrate the independence of certain pairs.
متن کاملNO : 4 TITLE : ‘ COMMUTATIVE ORDERS REVISITED ’ AUTHOR ( S ) : Professor Victoria Gould
This article studies commutative orders, that is, commutative semigroups having a semigroup of quotients. In a commutative order S, the square-cancellable elements S(S) constitute a well-behaved separable subsemigroup. Indeed, S(S) is also an order and has a maximum semigroup of quotients R, which is Clifford. We present a new characterisation of commutative orders in terms of semilattice decom...
متن کاملOn Some Finitary Conditions Arising from the Axiomatisability of Certain Classes of Monoid Acts
This article considers those monoids S satisfying one or both of the finitary properties (R) and (r), focussing for the most part on inverse monoids. These properties arise from questions of axiomatisability of classes of S-acts, and appear to be of interest in their own right. If S weakly right noetherian (WRN), that is, S has the ascending chain condition on right ideals, then certainly (r) h...
متن کامل