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  1. The strength of the tree theorem for pairs in reverse mathematics.Ludovic Patey - 2016 - Journal of Symbolic Logic 81 (4):1481-1499.
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  • Ramsey-type graph coloring and diagonal non-computability.Ludovic Patey - 2015 - Archive for Mathematical Logic 54 (7-8):899-914.
    A function is diagonally non-computable if it diagonalizes against the universal partial computable function. D.n.c. functions play a central role in algorithmic randomness and reverse mathematics. Flood and Towsner asked for which functions h, the principle stating the existence of an h-bounded d.n.c. function implies Ramsey-type weak König’s lemma. In this paper, we prove that for every computable order h, there exists an ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\omega}$$\end{document} -model of h-DNR which is not a not (...)
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  • Open questions about Ramsey-type statements in reverse mathematics.Ludovic Patey - 2016 - Bulletin of Symbolic Logic 22 (2):151-169.
    Ramsey’s theorem states that for any coloring of then-element subsets of ℕ with finitely many colors, there is an infinite setHsuch that alln-element subsets ofHhave the same color. The strength of consequences of Ramsey’s theorem has been extensively studied in reverse mathematics and under various reducibilities, namely, computable reducibility and uniform reducibility. Our understanding of the combinatorics of Ramsey’s theorem and its consequences has been greatly improved over the past decades. In this paper, we state some questions which naturally arose (...)
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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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  • Separating principles below WKL0.Stephen Flood & Henry Towsner - 2016 - Mathematical Logic Quarterly 62 (6):507-529.
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