Borel combinatorics fail in HYP

Abstract: We show that the Borel Dual Ramsey Theorem fails in HYP, regardless of the number of partitions k ≥ 2. Therefore, the Borel Dual Ramsey Theorem is not a statement of hyperarithmetic analysis. We also apply similar methods, namely construction of completely determined pseudo-Borel codes via decorating trees, to obtain results concerning some theorems about Borel graph coloring and the prisoner hat problem. Joint work with Henry Towsner and Rose Weisshaar.

logic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic