Local reflections of choice

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2025-06-02 DOI:10.1007/s10474-025-01533-3

C. Ryan-Smith

引用次数: 0

Abstract

Under the assumption of small violations of choice with seed \(S\) \((SVC(S))\), the failure of many choice principles reflect to local properties of \(S\), which can be a helpful characterisation for preservation proofs. We demonstrate the reflections of \(DC\), \(AC_\lambda\), \(PP\), and other important forms of choice. As a consequence, we show that if \(S\) is infinite then \(S\) can be partitioned into \(\omega\) many non-empty subsets.

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选择的本地反思

在具有种子\(S\)\((SVC(S))\)的选择的小违反假设下，许多选择原则的失效反映了\(S\)的局部性质，这可以帮助表征保存证明。我们展示了\(DC\)、\(AC_\lambda\)、\(PP\)和其他重要选择形式的反映。结果表明，如果\(S\)是无限的，那么\(S\)可以划分为\(\omega\)多个非空子集。

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

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.