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Uniform versions of some axioms of second order arithmetic

✍ Scribed by Nobuyuki Sakamoto; Takeshi Yamazaki

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 132 KB
Volume: 50
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200310122

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✦ Synopsis

Abstract

In this paper, we discuss uniform versions of some axioms of second order arithmetic in the context of higher order arithmetic. We prove that uniform versions of weak weak König's lemma WWKL and Σ^0^~1~ separation are equivalent to (∃^2^) over a suitable base theory of higher order arithmetic, where (∃^2^) is the assertion that there exists Φ^2^ such that Φ__f__^1^ = 0 if and only if ∃x^0^(fx = 0) for all f. We also prove that uniform versions of some well‐known theorems are equivalent to (∃^2^) or the axiom (Suslin) of the existence of the Suslin operator. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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