On the relationship between ATR 0 and

Journal of Symbolic Logic 61 (3):768-779 (1996)
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Abstract

We show that the theory ATR 0 is equivalent to a second-order generalization of the theory $\widehat{ID}_{ . As a result, ATR 0 is conservative over $\widehat{ID}_{ for arithmetic sentences, though proofs in ATR 0 can be much shorter than their $\widehat{ID}_{ counterparts

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10.2307/2275783

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Jeremy Avigad
Carnegie Mellon University

Citations of this work

Full and hat inductive definitions are equivalent in NBG.Kentaro Sato - 2015 - Archive for Mathematical Logic 54 (1-2):75-112.
Fixed point theories and dependent choice.Gerhard Jäger & Thomas Strahm - 2000 - Archive for Mathematical Logic 39 (7):493-508.

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Herbrand analyses.Wilfried Sieg - 1991 - Archive for Mathematical Logic 30 (5-6):409-441.

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