%0 Journal Article %A Avigad, Jeremy %D 1996 %T An Effective Proof that Open Sets are Ramsey %U https://kilthub.cmu.edu/articles/journal_contribution/An_Effective_Proof_that_Open_Sets_are_Ramsey/6490886 %R 10.1184/R1/6490886.v1 %2 https://kilthub.cmu.edu/ndownloader/files/11932313 %K Philosophy %X

Solovay has shown that if O is an open subset of P(ω) with code S and no infinite set avoids O , then there is an infinite set hyperarithmetic in S that lands in O . We provide a direct proof of this theorem that is easily formalizable in ATR0 .

%I Carnegie Mellon University