S-偏序集的公理化问题
Axiomatisability problems for S-posets
摘要：
设C是给定固定类型t的一类代数。与该类型相关联的是一阶语言L_t。然后人们可以问这样一个问题，什么时候类C可由L_t的句子公理化。在本文中，我们将考虑一类左S-偏序集在pomentum S（也就是说，一个幺半群S配备了一个偏序兼容的二元运算）的公理化问题。我们的目标是确定poms，使得某些范畴定义的类是可公理化的。我们考虑的类是自由的S-偏序集，投射的S-偏序集和类所产生的平坦性。Pervukhin和Stepanova在最近的一篇文章中研究了其中的一些案例。我们提出了一些一般的策略来确定公理化，从他们的结果类的弱PO-平坦和PO-平坦的S-偏序集将遵循。我们还考虑了一些以前没有检查过的类。
英文摘要：
Let C be a class of algebras of a given fixed type t. Associated with the type is a first order language L_t. One can then ask the question, when is the class C axiomatisable by sentences of L_t. 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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