测度代数的自同构群与自然数无限置换群相关的若干群的比较

整数的置换只导致图灵度的平凡自同构

Permutations of the integers induce only the trivial automorphism of the Turing degrees

设$π$是Cantor空间$2^ω$的同胚$φ$诱导的图灵度的自同构，使得$φ$保持所有Bernoulli测度.证明了$π$必定是平凡的。特别地，$ω$的置换只能导致图灵度的平凡自同构。

有序置换群的外自同构群

Outer Automorphism Groups of Ordered Permutation Groups

一个无限线性序集（S，<=）称为双齐次的，如果它的自同构群A（S）作用在它上面2-传递.我们证明了对于某个双齐次链（S，<=），任何群G都是自同构群A（S）的外自同构群G cong Out（A（S））.

传递扩展的通用结构自同构群

Transitive Extensions of Automorphism Groups of Generic Structures

研究传递扩展的存在性，发现仅当颜色数为2的幂时，边缘着色的k超图有传递扩展；k超 tournaments 在Cherlin意义上仅当k为偶数时存在传递扩展。

Infinite Limits of Finite-Dimensional Permutation Structures, and their Automorphism Groups: Between Model Theory and Combinatorics

In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is concerned with Cameron's problem of classifying the homogeneous structures in a language of finitely many linear orders, which we call finite-dimensional permutation structures. Towards this problem, we present a construction that we conjecture produces all such structures. Some evidence for this conjecture is given, including the classification of the homogene…

Twists and Twistability

Metrically homogeneous graphs are connected graphs which, when endowed with the path metric, are homogeneous as metric spaces. In this paper we introduce the concept of twisted automorphisms, a notion of isomorphism up to a permutation of the language. We find all permutations of the language which are associated with twisted automorphisms of metrically homogeneous graphs. For each non-trivial permutation of this type we also characterize the class of metrically homogeneous graphs which allow a twisted isomorphism associated with that permutation. The permutations we find are, remarkably, prec…

Permutation groups on countable vector spaces over prime fields

We describe all closed permutation groups which act on the set of vectors of a countable vector space $V$ over a prime field of odd order and which contain all automorphisms of $V$. In particular, we prove that their number is finite. These groups correspond, up to first-order interdefinability, precisely to all structures with a first-order definition in $V$.