Computable aspects of the Laver partition theorem

Abstract

The Laver Partition Theorem is a fundamental tool in the analysis of Laver and Hechler forcings. It is also connected to determinacy and the Galvin-Prikry theorem: indeed it can be seen as the common core of these two theorems. We study the reverse mathematics and Weihrauch degrees of the Laver Partition Theorem restricted to open and clopen sets. We obtain upper and lower bounds on the proof theoretic strength of this result, as well as a precise picture of the (arithmetical) Weihrauch degrees of the problems related to it.