Archive for Mathematical Logic

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

An effective proof that open sets are Ramsey

  • Jeremy Avigad


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 \(ATR_0\).


Open Subset Direct Proof Effective Proof 
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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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