Δ03-determinacy, comprehension and induction

被引：18

作者：

Medsalem, Medyahya Ould ^{[1
]}

Tanaka, Kazuyuki ^{[1
]}

机构：

[1] Tohoku Univ, Inst Math, Sendai, Miyagi 9808578, Japan

来源：

JOURNAL OF SYMBOLIC LOGIC | 2007年 / 72卷 / 02期

关键词：

WEAK AXIOMS; DETERMINACY; SUBSYSTEMS;

D O I：

10.2178/jsl/1185803618

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that each of Delta(1)(3)-CA(0) + Sigma(1)(3)-IND and Pi(1)(2)-CA(0)+Pi(1)(3)-Tl proves Delta(0)(3)-Det and that neither Sigma(1)(3)-IND nor Pi(1)(3)-Tl can be dropped. We also show that neither Delta(1)(3)-CA(0) + Sigma(1)(infinity)-IND nor Pi(1)(2)-CA(0) + Pi(1)(infinity)-Tl proves Sigma(0)(3)-Det. Moreover, we prove that none of Delta(1)(2)-CA(0). Sigma(1)(3)-IND and Pi(1)(2)-Tl is provable in Delta(1)(1)-Det(0) = ACA(0) + A(1)(1)-Det.

引用

页码：452 / 462

页数：11