Archive for Mathematical Logic 34 (6):345-375 (1995)

Abstract
We study elementary second order extensions of the theoryID 1 of non-iterated inductive definitions and the theoryPA Ω of Peano arithmetic with ordinals. We determine the exact proof-theoretic strength of those extensions and their natural subsystems, and we relate them to subsystems of analysis with arithmetic comprehension plusΠ 1 1 comprehension and bar induction without set parameters
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DOI 10.1007/BF02391553
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References found in this work BETA

Proof Theory.K. Schütte - 1977 - Springer Verlag.
Fixed Points in Peano Arithmetic with Ordinals.Gerhard Jäger - 1993 - Annals of Pure and Applied Logic 60 (2):119-132.
The Role of Parameters in Bar Rule and Bar Induction.Michael Rathjen - 1991 - Journal of Symbolic Logic 56 (2):715-730.

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Citations of this work BETA

Universes Over Frege Structures.Reinhard Kahle - 2003 - Annals of Pure and Applied Logic 119 (1-3):191-223.

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