The Galvin-Prikry theorem and set existen axioms

Kazuyuki Tanaka

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


H. Friedman observed the following phenomenon (or the 'theme' of Reverse Mathe in many branches of ordinary mathematics: When the theorem is proved from the right the axioms can be proved from the theorem. In this paper, we give an instance that the of Reverse Mathematics does not apply to the lightface statements, by demonstrating statement that all Σ11 partitions are Ramsey is deducible over the system ATR0 from the of Σ11 monotone inductive definition, but the reversal is not deducible over ATR0.

Original languageEnglish
Pages (from-to)81-104
Number of pages24
JournalAnnals of Pure and Applied Logic
Issue number1
Publication statusPublished - 1989 Mar 28
Externally publishedYes

ASJC Scopus subject areas

  • Logic


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