The Galvin-Prikry theorem and set existen axioms

Kazuyuki Tanaka

doi:10.1016/0168-0072(89)90066-3

The Galvin-Prikry theorem and set existen axioms

Kazuyuki Tanaka

Research output: Contribution to journal › Article

10 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	81-104
Number of pages	24
Journal	Annals of Pure and Applied Logic
Volume	42
Issue number	1
DOIs	https://doi.org/10.1016/0168-0072(89)90066-3
Publication status	Published - 1989 Mar 28
Externally published	Yes

ASJC Scopus subject areas

Logic

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