Infinite games in the Cantor space and subsystems of second order arithmetic

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Mathematical Logic Quarterly 53 (3):226-236 (2007)
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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 ⊢ equation image-Det* ↔ equation image-Det* ↔ WKL0.2. RCA0 ⊢ 2-Det* ↔ ACA0.3. RCA0 ⊢ equation image-Det* ↔ equation image-Det* ↔ equation image-Det ↔ equation image-Det ↔ ATR0.4. For 1 < k < ω, RCA0 ⊢ k-Det* ↔ k –1-Det.5. RCA0 ⊢ equation image-Det* ↔ equation image-Det.Here, Det* stands for the determinacy of infinite games in the Cantor space, and k is the collection of formulas built from equation image formulas by applying the difference operator k – 1 times.

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10.1002/malq.200610041

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Citations of this work

Open questions in reverse mathematics.Antonio Montalbán - 2011 - Bulletin of Symbolic Logic 17 (3):431-454.
Reverse mathematics: the playground of logic.Richard A. Shore - 2010 - Bulletin of Symbolic Logic 16 (3):378-402.

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