Variation on a theme of Schütte
Gerhard Jäger, Dieter Probst · Mathematical logic quarterly · 2004
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)