Second order theories with ordinals and elementary comprehension

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Archive for Mathematical Logic 34 (6):345-375 (1995)
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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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10.1007/bf02391553

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Citations of this work

Universes over Frege structures.Reinhard Kahle - 2003 - Annals of Pure and Applied Logic 119 (1-3):191-223.
The universal set and diagonalization in Frege structures.Reinhard Kahle - 2011 - Review of Symbolic Logic 4 (2):205-218.

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References found in this work

Proof theory.K. Schütte - 1977 - New York: Springer Verlag.
Fixed points in Peano arithmetic with ordinals.Gerhard Jäger - 1993 - Annals of Pure and Applied Logic 60 (2):119-132.
Beweistheorie vonKPN.Gerhard Jäger - 1980 - Archive for Mathematical Logic 20 (1-2):53-63.

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