论文标题
可确定集的拓扑特性在有序的亚伯利亚群体中的负担2
Topological properties of definable sets in ordered Abelian groups of burden 2
论文作者
论文摘要
我们在密集有序的负担负担的负担群体中获得了一组一体可确定集的拓扑结构的新结果。如果结构有2个负担2，并且可以定义一个无限的离散集D和一个密集的补充集X，则X的翻译必须见证独立财产。在最后一节中，给出了一个有序的阿贝尔群体负担2的明确示例，其中无限的离散集和密集的密度集可以定义。
We obtain some new results on the topology of unary definable sets in densely ordered Abelian groups of burden groups of burden 2. In the special case in which the structure has dp-rank 2, we show that the existence of an infinite definable discrete set precludes the definability of a set which is dense and codense in an interval, or of a set which is topologically like the Cantor middle-third set. If the structure has burden 2 and both an infinite discrete set D and a dense-codense set X are definable, then translates of X must witness the Independence Property. In the last section, an explicit example of an ordered Abelian group of burden 2 is given in which both an infinite discrete set and a dense-codense set are definable.
