Borel combinatorics fail in HYP

Henry Towsner; Rose Weisshaar; Linda Westrick

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arXiv · 2106.13330

Borel combinatorics fail in HYP

Henry Towsner·Rose Weisshaar·Linda Westrick

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Abstract

We characterize the completely determined Borel subsets of HYP as exactly the omega_1^{ck} subsets of HYP. As a result, HYP believes there is a Borel well-ordering of the reals, that the Borel Dual Ramsey Theorem fails, and that every Borel d-regular bipartite graph has a Borel perfect matching, among other examples. Therefore, the Borel Dual Ramsey Theorem and several theorems of descriptive combinatorics are not theories of hyperarithmetic analysis. In the case of the Borel Dual Ramsey Theorem, this answers a question of Astor, Dzhafarov, Montalban, Solomon & the third author.

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BibTeX RIS

Henry Towsner, Rose Weisshaar, Linda Westrick. 2021-06-24. Borel combinatorics fail in HYP. https://arxiv.org/abs/2106.13330

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