Partial orders and immunity in reverse mathematics

Article type: Research Article

Authors: Patey, Ludovic^{; *}

Affiliations: Laboratoire IRIF, Université Paris Diderot, Paris, France. ludovic.patey@computability.fr; http://ludovicpatey.com

Correspondence: [*] Corresponding author. ludovic.patey@computability.fr.

Abstract: We identify computability-theoretic properties enabling us to separate various statements about partial orders in reverse mathematics. We obtain simpler proofs of existing separations, and deduce new compound ones. This work is part of a larger program of unification of the separation proofs of various Ramsey-type theorems in reverse mathematics in order to obtain a better understanding of the combinatorics of Ramsey’s theorem and its consequences. We also answer a question of Murakami, Yamazaki and Yokoyama about pseudo Ramsey’s theorem for pairs.

Keywords: Ramsey’s theorem, partial orders, preservation, immunity, reverse mathematics

DOI: 10.3233/COM-170071

Journal: Computability, vol. 7, no. 4, pp. 323-339, 2018