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Subsystems of second-order arithmetic between RCA0and WKL0

✍ Scribed by Carl Mummert


Publisher
Springer
Year
2008
Tongue
English
Weight
161 KB
Volume
47
Category
Article
ISSN
0933-5846

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Determinacy of Wadge classes and subsyst
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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 RCA~0~\*, which consists of

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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. RCA~0~ ⊒ $ \Delta^0\_1 $‐Det\* ↔ $ \Sigma^0\_1 $‐Det\* ↔ WKL~0~. 2. RCA~0~ ⊒ ($ \Sigma^0\_1 $)2‐Det\* ↔