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arXiv 1504.01405math.LO
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强约化和组合原理

Strong reductions and combinatorial principles

Damir D. Dzhafarov

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摘要：

本文是对二阶算术的$Π^1_2$语句之间的强可约性的日益增长的调查的贡献，被视为传统的逆向数学分析的扩展。我们回答几个问题的Hirschfeldt和Jockusch（出现）关于统一和强大的可计算减少各种组合原则有关拉姆齐定理对。在其他结果中，我们建立的原则$\mathsf{SRT}^2_2$是不一致或强可计算约简为$\mathsf{D}^2_{<\infty}$，$\mathsf{COH}$是不一致约简为$\mathsf{D}^2_{<\infty}$，$\mathsf{COH}$是不强可约简为$\mathsf{D}^2_2$。后者也扩展了Dzhafarov（2015）的先前结果。我们引入了一些新的技术，用于控制我们在我们的论点中构建的问题和解决方案的组合和可计算性理论属性。

英文摘要：

This paper is a contribution to the growing investigation of strong reducibilities between $Π^1_2$ statements of second-order arithmetic, viewed as an extension of the traditional analysis of reverse mathematics. We answer several questions of Hirschfeldt and Jockusch (to appear) about uniform and strong computable reductions between various combinatorial principles related to Ramsey's theorem for pairs. Among other results, we establish that the principle $\mathsf{SRT}^2_2$ is not uniformly or strongly computably reducible to $\mathsf{D}^2_{<\infty}$, that $\mathsf{COH}$ is not uniformly reducible to $\mathsf{D}^2_{<\infty}$, and that $\mathsf{COH}$ is not strongly reducible to $\mathsf{D}^2_2$. The latter also extends a prior result of Dzhafarov (2015). We introduce a number of new techniques for controlling the combinatorial and computability-theoretic properties of the problems and solutions we construct in our arguments.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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