连通po-广群胚的半生成簇中的直接不可分解
Directly Indecomposables in Semidegenerate Varieties of Connected po-Groupoids
摘要：
我们研究具有术语可定义的偏序集结构的变种，“po-广群胚”。已知连通偏序集具有严格加细性质（SRP）。在[arXiv：0808.1860v1 [math.LO]]中证明了具有SRP的半生成簇具有可定义的因子同余，并且如果相似类型是有限的，则直接不可分解的可由一组一阶句子公理化。我们得到了这样一个集的半生成品种的连通po-广群，并表明其量词复杂性是有界的一般。
英文摘要：
We study varieties with a term-definable poset structure, "po-groupoids". It is known that connected posets have the "strict refinement property" (SRP). In [arXiv:0808.1860v1 [math.LO]] it is proved that semidegenerate varieties with the SRP have definable factor congruences and if the similarity type is finite, directly indecomposables are axiomatizable by a set of first-order sentences. We obtain such a set for semidegenerate varieties of connected po-groupoids and show its quantifier complexity is bounded in general.
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