Determinacy of Wadge classes and subsystems of second order arithmetic

Mathematical Logic Quarterly 55 (2):154-176 (2009)
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Abstract

In this paper we study the logical strength of the determinacy of infinite binary games in terms of second order arithmetic. We define new determinacy schemata inspired by the Wadge classes of Polish spaces and show the following equivalences over the system RCA0*, which consists of the axioms of discrete ordered semi‐rings with exponentiation, Δ10 comprehension and Π00 induction, and which is known as a weaker system than the popularbase theory RCA0: 1. Bisep(Δ10, Σ10)‐Det* ↔ WKL0, 2. Bisep(Δ10, Σ20)‐Det* ↔ ATR0 + Σ11 induction, 3. Bisep(Σ10, Σ20)‐Det* ↔ Sep(Σ10, Σ20)‐Det* ↔ Π11‐CA0, 4. Bisep(Δ20, Σ20)‐Det* ↔ Π11‐TR0, where Det* stands for the determinacy of infinite games in the Cantor space (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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10.1002/malq.200710081

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Citations of this work

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Full and hat inductive definitions are equivalent in NBG.Kentaro Sato - 2015 - Archive for Mathematical Logic 54 (1-2):75-112.

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References found in this work

Factorization of polynomials and °1 induction.S. G. Simpson - 1986 - Annals of Pure and Applied Logic 31:289.
Weak axioms of determinacy and subsystems of analysis II.Kazuyuki Tanaka - 1991 - Annals of Pure and Applied Logic 52 (1-2):181-193.
Weak axioms of determinacy and subsystems of analysis I: δ20 games.Kazuyuki Tanaka - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (6):481-491.

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