Axiomatisability problems for S-posets

作者：Gould Victoria^*; Shaheen Lubna

来源：Semigroup Forum, 2011, 82(2): 199-228.

DOI：10.1007/s00233-010-9273-7

• Axiomatisability
• Free
• Projective
• Flat
• S-posets

Let C be a class of ordered algebras of a given fixed type tau. Associated with the type is a first order language L (tau) , 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 L (tau) ? 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.

• 出版日期2011-4