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Archive for Mathematical Logic

, Volume 37, Issue 4, pp 235–240 | Cite as

An effective proof that open sets are Ramsey

  • Jeremy Avigad

Abstract.

Solovay has shown that if \(\cal{O}\) is an open subset of \(P(\omega)\) with code \(S\) and no infinite set avoids \(\cal{O}\), then there is an infinite set hyperarithmetic in \(S\) that lands in \(\cal{O}\). We provide a direct proof of this theorem that is easily formalizable in \(ATR_0\).

Keywords

Open Subset Direct Proof Effective Proof 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jeremy Avigad
    • 1
  1. 1. Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213, USA US

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