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The Recursively Mahlo Property in Second Order Arithmetic

✍ Scribed by Michael Rathjen

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
388 KB
Volume
42
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

The paper characterizes the second order arithmetic theorems of a set theory that features a recursively Mahlo universe; thereby complementing prior proof‐theoretic investigations on this notion. It is shown that the property of being recursively Mahlo corresponds to a certain kind of β‐model reflection in second order arithmetic. Further, this leads to a characterization of the reals recursively computable in the superjump functional.

Mathematics Subject Classification: 03F35, 03F15, 03E70.

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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\* ↔