Concerning Keisler measures over ultraproducts

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2024-07-09 DOI:10.1016/j.apal.2024.103492

Kyle Gannon

引用次数: 0

Abstract

As consequence of the VC theorem, any pseudo-finite measure over an NIP ultraproduct is generically stable. We demonstrate a converse of this theorem and prove that any finitely approximable measure over an ultraproduct is itself pseudo-finite (even without the NIP assumption). We also analyze the connection between the Morley product and the pseudo-finite product. In particular, we show that if μ is definable and both μ and ν are pseudo-finite, then the Morley product of μ and ν agrees with the pseudo-finite product of μ and ν. Using this observation, we construct generically stable idempotent measures on pseudo-finite NIP groups.

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关于超积物上的凯斯勒量纲

根据 VC 定理，NIP 超积上的任何伪有限度量都是一般稳定的。我们证明了这一定理的逆定理，并证明超积上的任何有限可近似度量本身都是伪无限的（即使没有 NIP 假设）。我们还分析了莫利积和伪无限积之间的联系。特别是，我们证明，如果是可定义的，并且和都是伪无限的，那么和的莫利积与和的伪无限积是一致的。利用这一观察结果，我们构建了伪无限 NIP 群上一般稳定的幂级数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.