一元 NIP 理论中的不可分性

Samuel Braunfeld, Michael C. Laskowski
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引用次数: 0

摘要

首先,我们用indiscernibles对单元 NIP 进行了几种描述,这与之前用有限可满足性的行为对单元 NIP 进行描述如出一辙。其次,我们研究了遗传类和完备理论中的(一元)距离性。在这里,通过有限组合论,我们证明了一个意味着每个平面图都允许远端扩展的结果。最后,我们证明了一个结果,它意味着没有一个一元 NIP 理论能解释一个无限群,并指出了一个没有远端展开的(一元)稳定理论的例子,它不解释一个无限群。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Indiscernibles in monadically NIP theories
We prove various results around indiscernibles in monadically NIP theories. First, we provide several characterizations of monadic NIP in terms of indiscernibles, mirroring previous characterizations in terms of the behavior of finite satisfiability. Second, we study (monadic) distality in hereditary classes and complete theories. Here, via finite combinatorics, we prove a result implying that every planar graph admits a distal expansion. Finally, we prove a result implying that no monadically NIP theory interprets an infinite group, and note an example of a (monadically) stable theory with no distal expansion that does not interpret an infinite group.
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