在大的外部可定义集合上

IF 1.1 2区数学 Q1 MATHEMATICS

Journal of the Institute of Mathematics of Jussieu Pub Date : 2023-12-04 DOI:10.1017/s1474748023000464

Martin Bays, Omer Ben-Neria, Itay Kaplan, Pierre Simon

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引用次数: 0

摘要

我们研究了$\ \ _1$的有限子集的协终系统。我们表明，虽然这样的系统可以是NIP，但它们不能在NIP结构中定义。我们对Chernikov和Simon 2013年提出的一个问题给出了一个肯定的答案:在NIP理论中，任何不可数的外部可定义集合都包含一个无限的可定义子集。对于较大的基数也有类似的结果。

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ON LARGE EXTERNALLY DEFINABLE SETS IN NIP

We study cofinal systems of finite subsets of

$\omega _1$

. We show that while such systems can be NIP, they cannot be defined in an NIP structure. We deduce a positive answer to a question of Chernikov and Simon from 2013: In an NIP theory, any uncountable externally definable set contains an infinite definable subset. A similar result holds for larger cardinals.

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来源期刊

Journal of the Institute of Mathematics of Jussieu 数学-数学

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.