On the Relationships between $ATR_0$ And $\widehat{ID}_{< \omega}$
Avigad, Jeremy
J. Symbolic Logic, Tome 61 (1996) no. 1, p. 768-779 / Harvested from Project Euclid
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We show that the theory $ATR_0$ is equivalent to a second-order generalization of the theory $\widehat{ID}_{<\omega}$. As a result, $ATR_0$ is conservative over $\widehat{ID}_{<\omega}$ for arithmetic sentences, though proofs in $ATR_0$ can be much shorter than their $\widehat{ID}_{<\omega}$ counterparts.
Publié le : 1996-09-14
Classification:  
@article{1183745075,
     author = {Avigad, Jeremy},
     title = {On the Relationships between $ATR\_0$ And $\widehat{ID}\_{< \omega}$},
     journal = {J. Symbolic Logic},
     volume = {61},
     number = {1},
     year = {1996},
     pages = { 768-779},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745075}
}

Avigad, Jeremy. On the Relationships between $ATR_0$ And $\widehat{ID}_{< \omega}$. J. Symbolic Logic, Tome 61 (1996) no. 1, pp.  768-779. http://gdmltest.u-ga.fr/item/1183745075/