卡尔森-辛普森引理及其在逆向数学中的应用

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2023-10-01 DOI:10.1016/j.apal.2023.103287

Paul-Elliot Angles d'Auriac , Lu Liu , Bastien Mignoty , Ludovic Patey

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引用次数: 0

摘要

我们研究了由Carlson和Simpson提出的Hales-Jewett定理的无穷扩展的逆数学。这些定理在拉姆齐理论中有多种应用，如无三角形图的有限大拉姆齐度的存在性，或对偶拉姆齐定理。我们特别证明了开对偶Ramsey定理在ACA0+中成立。

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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Carlson-Simpson's lemma and applications in reverse mathematics

We study the reverse mathematics of infinitary extensions of the Hales-Jewett theorem, due to Carlson and Simpson. These theorems have multiple applications in Ramsey's theory, such as the existence of finite big Ramsey degrees for the triangle-free graph, or the Dual Ramsey theorem. We show in particular that the Open Dual Ramsey theorem holds in ${ACA}_{0}^{+}$ .

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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.