Variation on a theme of Schutte

Mathematical Logic Quarterly 50 (3):258 (2004)
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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 ≺

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References found in this work

On the relationship between ATR 0 and.Jeremy Avigad - 1996 - Journal of Symbolic Logic 61 (3):768-779.
Incompleteness along paths in progressions of theories.S. Feferman & C. Spector - 1962 - Journal of Symbolic Logic 27 (4):383-390.
On the relationships between ATR0 and $\widehat{ID}_{.Jeremy Avigad - 1996 - Journal of Symbolic Logic 61 (3):768 - 779.
Wellordering proofs for metapredicative Mahlo.Thomas Strahm - 2002 - Journal of Symbolic Logic 67 (1):260-278.

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