Automorphism groups of prime models, and invariant measures

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2025-02-28 DOI:10.1016/j.apal.2025.103568

Anand Pillay

引用次数: 0

Abstract

We adapt the notion from [7] and [2] of a (relatively) definable subset of

A u t (M)

when M is a saturated structure, to the case

A u t (M / A)

when M is atomic and strongly ω-homogeneous (over a set A). We discuss the existence and uniqueness of invariant measures on the Boolean algebra of definable subsets of

A u t (M / A)

. For example when T is stable, we have existence and uniqueness.

We also discuss the compatibility of our definability notions with definable Galois cohomology from [12] and differential Galois theory.

查看原文本刊更多论文

素数模型的自同构群与不变测度

我们将M是饱和结构时Aut(M)的一个（相对）可定义子集的[7]和[2]的概念，引入到M是原子且强ω齐次（在集合a上）时Aut（M/ a）的情况。我们讨论了Aut（M/ a）的可定义子集布尔代数上不变测度的存在性和唯一性。例如，当T稳定时，我们有存在唯一性。我们还从[12]和微分伽罗瓦理论讨论了可定义性概念与可定义伽罗瓦上同调的相容性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.