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

Kazuyuki Tanaka

doi:10.1016/0168-0072(91)90045-N

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

Kazuyuki Tanaka

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	181-193
Number of pages	13
Journal	Annals of Pure and Applied Logic
Volume	52
Issue number	1-2
DOIs	https://doi.org/10.1016/0168-0072(91)90045-N
Publication status	Published - 1991 Apr 15

ASJC Scopus subject areas

Logic

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