Infinite games and transfinite recursion of multiple inductive definitions

Keisuke Yoshii, Kazuyuki Tanaka

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

The purpose of this research is to investigate the logical strength of weak determinacy of Gale-Stewart games from the standpoint of reverse mathematics. It is known that the determinacy of sets (open sets) is equivalent to system ATR 0 and that of Σ 2 0 corresponds to the axiom of Σ 1 1 inductive definitions. Recently, much effort has been made to characterize the determinacy of game classes above Σ 2 0 within second order arithmetic. In this paper, we show that for any k ε ω, the determinacy of Δ((Σ 2 0) k+1) sets is equivalent to the axiom of transfinite recursion of Σ 1 1 inductive definitions with k operators, denote [Σ 1 1] k -IDTR. Here, (Σ 2 0) k+1 is the difference class of k + 1 Σ 2 0 sets and Δ((Σ 2 0) k+1) is the conjunction of (Σ 2 0) k+1 and co-(Σ 2 0) k+1.

本文言語English
ホスト出版物のタイトルHow the World Computes - Turing Centenary Conference and 8th Conference on Computability in Europe, CiE 2012, Proceedings
ページ374-383
ページ数10
DOI
出版ステータスPublished - 2012
イベントTuring Centenary Conference and 8th Conference on Computability in Europe, CiE 2012 - Cambridge, United Kingdom
継続期間: 2012 6 182012 6 23

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
7318 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

OtherTuring Centenary Conference and 8th Conference on Computability in Europe, CiE 2012
国/地域United Kingdom
CityCambridge
Period12/6/1812/6/23

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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