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Ramsey's theorem in bounded arithmetic

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Computer Science Logic (CSL 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 533))

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Abstract

We shall show that the finite Ramsey theorem as a Δ0 schema is provable in IΔ 0+Ω1. As a consequence we get that propositional formulas expressing the finite Ramsey theorem have polynomial-size bounded-depth Frege proofs.

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Authors and Affiliations

  1. Mathematical Institute, Žitná 25, Praha 1, Czechoslovakia

    Pavel Pudlák

Authors
  1. Pavel Pudlák
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Editor information

Egon Börger Hans Kleine Büning Michael M. Richter Wolfgang Schönfeld

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© 1991 Springer-Verlag Berlin Heidelberg

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Pudlák, P. (1991). Ramsey's theorem in bounded arithmetic. In: Börger, E., Kleine Büning, H., Richter, M.M., Schönfeld, W. (eds) Computer Science Logic. CSL 1990. Lecture Notes in Computer Science, vol 533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54487-9_67

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  • DOI: https://doi.org/10.1007/3-540-54487-9_67

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54487-6

  • Online ISBN: 978-3-540-38401-4

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