几乎自由有限覆盖
Almost-free finite covers
摘要：
有限覆盖是一种从简单结构构建新结构的技术。研究有限覆盖的最初动机是Zilber的阶梯定理，它描述了如何通过一系列覆盖从严格极小集建立完全范畴结构。设W是一阶结构，r是W上的Aut（W）-同余.本文定义了W关于r的几乎自由有限覆盖，并给出了如何构造它们的方法。这些是自由有限覆盖的推广。Evans和Hrushovski在“On the automorphism groups of finite covers”一文中的一个结果的一个推论是：W的任何有限覆盖，如果约束群都等于一个简单的非交换置换群，则关于W上的某个r几乎是自由的。我们的主要结果给出了W的主有限覆盖的核在W上的Aut（W）-同余的描述（直到同构），其中绑定群在任意点等于一个简单的非交换正则置换群G.然后，我们分析了几乎自由有限覆盖的集合的有序的n-元组的不同的元素从一个可数集欧米茄，视为一个结构的自同构群等于Sym（欧米茄），我们显示了一个结果的双解释性。
英文摘要：
Finite covers are a technique for building new structures from simpler ones. The original motivation to study finite covers is in the Ladder theorem of Zilber which describes how totally categorical structures are built from strictly minimal sets by a sequence of covers. Let W be a first-order structure and r be an Aut(W)-congruence on W. In this paper we define the almost-free finite covers of W with respect to r, and we show how to construct them. These are a generalization of free finite covers. A consequence of a result of Evans and Hrushovski in the paper "On the automorphism groups of finite covers" is that any finite cover of W with binding groups all equal to a simple non-abelian permutation group is almost-free with respect to some r on W. Our main result gives a description (up to isomorphism) in terms of the Aut(W)-congruences on W of the kernels of principal finite covers of W with bindings groups equal at any point to a simple non-abelian regular permutation group G. Then we analyze almost-free finite covers of the set of ordered n-tuples of distinct elements from a countable set Omega, regarded as a structure with automorphism group equal to the Sym(Omega) and we show a result of biinterpretability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
