论文标题
关于$ω$ - 分类的Hrushovski构造的不可估量
On the non-measurability of $ω$-categorical Hrushovski constructions
论文作者
论文摘要
我们研究$ω$ - 分类$ MS $ - 可容纳结构。我们的主要结果是一类$ω$ - 类别的Hrushovski构造，有限的$ su $ -rank不是$ ms $ - 乘以。这些结果补充了埃文斯对Macpherson和Elwes的猜想的工作。与埃文斯（Evans）的工作相反，我们的结构可能满足所有$ n $的独立$ n $ amalgamation。我们还在$ω$ -STAGILORICAL $ MS $ - 衡量结构的背景下证明了一些一般结果。首先，在这些结构中，可以选择$ ms $ dimension-Measure中的尺寸为$ su $ rank。其次，非叉式独立性意味着该措施中概率独立性的一种形式。后者是由Hrushovski的更一般未发表的结果遵循的，但我们提供了一个独立的证据。
We study $ω$-categorical $MS$-measurable structures. Our main result is that a class of $ω$-categorical Hrushovski constructions, supersimple of finite $SU$-rank is not $MS$-measurable. These results complement the work of Evans on a conjecture of Macpherson and Elwes. In contrast to Evans' work, our structures may satisfy independent $n$-amalgamation for all $n$. We also prove some general results in the context of $ω$-categorical $MS$-measurable structures. Firstly, in these structures, the dimension in the $MS$-dimension-measure can be chosen to be $SU$-rank. Secondly, non-forking independence implies a form of probabilistic independence in the measure. The latter follows from more general unpublished results of Hrushovski, but we provide a self-contained proof.
