选择层次原则中的Hindman定理

IF 0.9 1区数学 Q1 LOGIC

Journal of Mathematical Logic Pub Date : 2022-03-11 DOI:10.1142/s0219061323500022

David J. Fern'andez-Bret'on

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引用次数: 2

摘要

在$\mathsf｛ZF｝$的上下文中，我们分析了无限集上Hindman有限并集定理的一个版本，它通常需要证明选择公理。我们建立了该语句与各种经典弱选择原则之间的蕴涵关系，从而准确地将该语句的强度定位为$\mathsf{AC}$的弱形式。

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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Hindman's theorem in the hierarchy of choice principles

In the context of $\mathsf{ZF}$, we analyze a version of Hindman's finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the $\mathsf{AC}$.

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来源期刊

Journal of Mathematical Logic MATHEMATICS-LOGIC

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Logic (JML) provides an important forum for the communication of original contributions in all areas of mathematical logic and its applications. It aims at publishing papers at the highest level of mathematical creativity and sophistication. JML intends to represent the most important and innovative developments in the subject.