WEAK AXIOMS OF DETERMINACY AND SUBSYSTEMS OF ANALYSIS II (SIGMA-2(0) GAMES)

被引：26

作者：

TANAKA, K

机构：

[1] Department of Information Science, Tokyo Institute of Technology, Meguro-ku, Tokyo, 152, Ookayama

来源：

ANNALS OF PURE AND APPLIED LOGIC | 1991年 / 52卷 / 1-2期

关键词：

D O I：

10.1016/0168-0072(91)90045-N

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In [10], we have shown that the statement that all SIGMA-1(1) partitions are Ramsey is deducible over ATR0 from the axiom of SIGMA-1(1) monotone inductive definition, but the reversal needs needs PI-1(1)-CA0 rather than ATR0. By contrast, we show in this paper that the statement that all SIGMA-2(0) games are determinate is also deducible over ATR0 from the axiom of SIGMA-1(1) 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.

引用

页码：181 / 193

页数：13

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