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arXiv · 1602.03784

$\mathsf{RT}_2^2$ does not imply $\mathsf{WKL}_0$

Lu Liu
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Abstract

We prove that $\mathsf{RCA}_0+\mathsf{RT}_2^2\not\rightarrow \mathsf{WKL}_0$ by showing that for any set $C$ not of PA-degree and any set $A$, there exists an infinite subset $G$ of $A$ or $\bar{A}$, such that $G\oplus C$ is also not of PA-degree.

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Lu Liu. 2016-02-11. $\mathsf{RT}_2^2$ does not imply $\mathsf{WKL}_0$. https://arxiv.org/abs/1602.03784

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