A note on the cardinality of definable families of sets in o-minimal structures

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2024-09-22 DOI:10.1002/malq.202300030

Pablo Andújar Guerrero

引用次数: 0

Abstract

We prove that any definable family of subsets of a definable infinite set $A$ in an o-minimal structure has cardinality at most $| A |$ . We derive some consequences in terms of counting definable types and existence of definable topological spaces.

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关于0 -极小结构中可定义集合族的基数性的注记

证明了0 -极小结构中任意可定义无限集a $ a $的可定义子集族的基数不超过| a |$ | a |$。我们从可定义类型的计数和可定义拓扑空间的存在性方面得到了一些结果。

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

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.