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Variation on a theme of Schütte
Author(s) -
Jäger Gerhard,
Probst Dieter
Publication year - 2004
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310097
Subject(s) - variation (astronomy) , mathematics , theme (computing) , computer science , physics , world wide web , astrophysics
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)