厄尔多斯-莫泽尔和 IΣ2

IF 0.8 2区数学 Q2 MATHEMATICS

Israel Journal of Mathematics Pub Date : 2024-08-04 DOI:10.1007/s11856-024-2643-8

Henry Towsner, Keita Yokoyama

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引用次数: 0

摘要

已知拉姆齐定理的一阶部分对于任意颜色数的配对恰好是 BΣ03。我们将其与已知的拉姆齐配对定理分为较弱的原理，即 EM（厄尔多斯-莫泽原理）和 ADS（升序-降序原理）进行比较：我们证明，超出 IΣ02 的额外强度完全归因于 ADS 的任意颜色类似物。具体地说，我们证明任意颜色数的 ADS 意味着 BΣ03 ，而任意颜色数的 EM 对 IΣ02 是 Π11 保守的，它并不意味着 IΣ02。

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Erdős–Moser and IΣ2

The first-order part of Ramsey’s theorem for pairs with an arbitrary number of colors is known to be precisely BΣ ⁰₃ . We compare this to the known division of Ramsey’s theorem for pairs into the weaker principles, EM (the Erdős–Moser principle) and ADS (the ascending-descending sequence principle): we show that the additional strength beyond IΣ ⁰₂ is entirely due to the arbitrary color analog of ADS.

Specifically, we show that ADS for an arbitrary number of colors implies BΣ ⁰₃ while EM for an arbitrary number of colors is Π ¹₁ -conservative over IΣ ⁰₂ and it does not imply IΣ ⁰₂ .

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来源期刊

Israel Journal of Mathematics 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.