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Variation on a theme of Schütte

✍ Scribed by Gerhard Jäger; Dieter Probst

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
125 KB
Volume
50
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Let ≺ be a primitive recursive well‐ordering on the natural numbers and assume that its order‐type is greater than or equal to the proof‐theoretic ordinal of the theory T. We show that the proof‐theoretic strength of T is not increased if we add the negation of the statement which formalizes transfinite induction along ≺. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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