A recursive coloring function without $\Pi_3^0$ solution for Hindman theorem

Yuke Liao

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arXiv · 2206.06859

A recursive coloring function without $\Pi_3^0$ solution for Hindman theorem

Yuke Liao

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Abstract

We show that there exists a recursive coloring function $c$ such that any $\Pi^0_3$ set is not a solution to $c$ for Hindman's theorem. We also show that there exists a recursive coloring function $c$ such that any $\Delta^0_3$ set is not a solution to $c$ for Hindman's theorem restricted on sum of at most three numbers.

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BibTeX RIS

Yuke Liao. 2022-06-14. A recursive coloring function without $\Pi_3^0$ solution for Hindman theorem. https://arxiv.org/abs/2206.06859

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