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  1. The Weakness of the Pigeonhole Principle Under Hyperarithmetical Reductions.Benoit Monin & Ludovic Patey - forthcoming - Journal of Mathematical Logic:2150013.
    The infinite pigeonhole principle for 2-partitions asserts the existence, for every set [Formula: see text], of an infinite subset of [Formula: see text] or of its complement. In this paper, we study the infinite pigeonhole principle from a computability-theoretic viewpoint. We prove in particular that [Formula: see text] admits strong cone avoidance for arithmetical and hyperarithmetical reductions. We also prove the existence, for every [Formula: see text] set, of an infinite low[Formula: see text] subset of it or its complement. This (...)
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  • Degrees Bounding Principles and Universal Instances in Reverse Mathematics.Ludovic Patey - 2015 - Annals of Pure and Applied Logic 166 (11):1165-1185.
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  • The Definability Strength of Combinatorial Principles.Wei Wang - 2016 - Journal of Symbolic Logic 81 (4):1531-1554.
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  • Open Questions About Ramsey-Type Statements in Reverse Mathematics.Ludovic Patey - 2016 - Bulletin of Symbolic Logic 22 (2):151-169.
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