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Partial Orders and Immunity in Reverse Mathematics

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Pursuit of the Universal (CiE 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9709))

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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.

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Author information

Authors and Affiliations

  1. Laboratoire PPS, Université Paris Diderot, Paris, France

    Ludovic Patey

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  1. Ludovic Patey
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Correspondence to Ludovic Patey .

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Editors and Affiliations

  1. Swansea University, Swansea, United Kingdom

    Arnold Beckmann

  2. Université Paris-Diderot - Paris 7, Paris, France

    Laurent Bienvenu

  3. University of South Florida, Tampa, Florida, USA

    Nataša Jonoska

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Patey, L. (2016). Partial Orders and Immunity in Reverse Mathematics. In: Beckmann, A., Bienvenu, L., Jonoska, N. (eds) Pursuit of the Universal. CiE 2016. Lecture Notes in Computer Science(), vol 9709. Springer, Cham. https://doi.org/10.1007/978-3-319-40189-8_36

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  • DOI: https://doi.org/10.1007/978-3-319-40189-8_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40188-1

  • Online ISBN: 978-3-319-40189-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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