The Role of Parameters in Bar Rule and Bar Induction

Rathjen, Michael

J. Symbolic Logic, Tome 56 (1991) no. 1, p. 715-730 / Harvested from Project Euclid

Résumé

For several subsystems of second order arithmetic $\mathbf{T}$ we show that the proof-theoretic strength of $\mathbf{T}$ + (bar rule) can be characterized in terms of $\mathbf{T} +$ (bar induction)$^\square$, where the latter scheme arises from the scheme of bar induction by restricting it to well-orderings with no parameters. In addition, we demonstrate that $\mathbf{ACA}^+_0, \mathbf{ACA}_0 +$ (bar rule) and $\mathbf{ACA}_0 +$ (bar induction)$^\square$ prove the same $\Pi^1_1$-sentences.

Publié le : 1991-06-14
Classification:

@article{1183743670,
     author = {Rathjen, Michael},
     title = {The Role of Parameters in Bar Rule and Bar Induction},
     journal = {J. Symbolic Logic},
     volume = {56},
     number = {1},
     year = {1991},
     pages = { 715-730},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183743670}
}

Rathjen, Michael. The Role of Parameters in Bar Rule and Bar Induction. J. Symbolic Logic, Tome 56 (1991) no. 1, pp.  715-730. http://gdmltest.u-ga.fr/item/1183743670/