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Reverse mathematics and colorings of hypergraphs

  • Caleb Davis
  • Jeffry HirstEmail author
  • Jake Pardo
  • Tim Ransom
Article
  • 9 Downloads

Abstract

Working in subsystems of second order arithmetic, we formulate several representations for hypergraphs. We then prove the equivalence of various vertex coloring theorems to \({\textsf {WKL}}_0\), \({\textsf {ACA}}_0\), and \({\varPi ^1_1 \text {-}}{\textsf {CA}}_0\).

Keywords

Reverse mathematics Hypergraph Vertex Coloring 

Mathematics Subject Classification

03B30 03F35 05C15 

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Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Caleb Davis
    • 1
  • Jeffry Hirst
    • 1
    Email author
  • Jake Pardo
    • 1
  • Tim Ransom
    • 2
  1. 1.Department of Mathematical SciencesAppalachian State UniversityBooneUSA
  2. 2.Computer Science DivisionClemson UniversityClemsonUSA

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