Infinite games in the Cantor space and subsystems of second order arithmetic |
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Authors: | Takako Nemoto MedYahya Ould MedSalem Kazuyuki Tanaka |
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Affiliation: | Mathematical Institute, Tohoku University, Sendai, 980‐8578, Japan |
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Abstract: | In this paper we study the determinacy strength of infinite games in the Cantor space and compare them with their counterparts in the Baire space. We show the following theorems: 1. RCA0 ? ‐Det* ? ‐Det* ? WKL0. 2. RCA0 ? ( )2‐Det* ? ACA0. 3. RCA0 ? ‐Det* ? ‐Det* ? ‐Det ? ‐Det ? ATR0. 4. For 1 < k < ω, RCA0 ? ( )k ‐Det* ? ( )k –1‐Det. 5. RCA0 ? ‐Det* ? ‐Det. Here, Det* (respectively Det) stands for the determinacy of infinite games in the Cantor space (respectively the Baire space), and ( )k is the collection of formulas built from formulas by applying the difference operator k – 1 times. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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Keywords: | Reverse mathematics determinacy second order arithmetic |
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