The strength of infinitary Ramseyan principles can be accessed by their densities
The strength of infinitary Ramseyan principles can be accessed by their densities
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无限拉姆塞扬原理的强度可以通过其密度来获得
DOI：
10.1016/j.apal.2017.03.005
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Weiermann
中科院分区：
文献类型：
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作者：
A. Bovykin;A. Weiermann
在这篇文章中，我们对三个无穷Ramseyan命题进行了模型论研究：关于配对和双色的无限Ramsey定理(RT22)，关于配对的正则Ramsey定理(CRT2)和关于配对的回归Ramsey定理(RegRT2)。我们用它们的一阶迭代形式的强度来近似这些原理的逻辑强度，也就是众所周知的密度原理。然后，我们利用Peano算法模型的强初始段，本着Paris和Kirby的经典文章的精神，考察了它们的逻辑强度，从而从理论上重新证明了旧的结果模型。本文最后讨论了密度的两个进一步扩展。一个是进一步研究关于对的Ramsey定理的强度。另一个是关于标准Ramsey函数R2的渐近性.
In this article, we conduct a model-theoretic investigation of three infinitary Ramseyan statements: the Infinite Ramsey Theorem for pairs and two colours (RT 2 2), the Canonical Ramsey Theorem for pairs (CRT 2) and the Regressive Ramsey Theorem for pairs (RegRT 2). We approximate the logical strength of these principles by the strength of their first-order iterated versions, known as density principles. We then investigate their logical strength using strong initial segments of models of Peano Arithmetic, in the spirit of the classical article by Paris and Kirby, hereby re-proving old results model-theoretically. The article is concluded by a discussion of two further outreaches of densities. One is a further investigation of the strength of the Ramsey Theorem for pairs. The other deals with the asymptotics of the standard Ramsey function R 2 2.
关于拉姆齐对定理
DOI：
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发表时间：
2011
期刊：
影响因子：
--
作者：
Keita Yokoyama;Sam Sanders;Takahiro Yamamoto;坂井哲;A. Shioura;Yu Kawakami;S. Kusuoka and S. Liang;Keita Yokoyama
通讯作者：
Keita Yokoyama