Weak axioms of determinacy and subsystems of analysis II (∑02 games)

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23 Citations (Scopus)

Abstract

In [10], we have shown that the statement that all ∑11 partitions are Ramsey is deducible over ATR0 from the axiom of ∑11 monotone inductive definition,but the reversal needs P{cyrillic}11-CA0 rather than ATR0. By contrast, we show in this paper that the statement that all ∑02 games are determinate is also deducible over ATR0 from the axiom of ∑11 monotone inductive definition, but the reversal is provable even in ACA0. These results illuminate the substantial differences among lightface theorems which can not be observed in boldface.

Original languageEnglish
Pages (from-to)181-193
Number of pages13
JournalAnnals of Pure and Applied Logic
Volume52
Issue number1-2
DOIs
Publication statusPublished - 1991 Apr 15

ASJC Scopus subject areas

  • Logic

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