An intensional fixed point theory over first order arithmetic

Annals of Pure and Applied Logic 128 (1-3):197-213 (2004)

Abstract
The purpose of this article is to present a new theory for fixed points over arithmetic which allows the building up of fixed points in a very nested and entangled way. But in spite of its great expressive power we can show that the proof-theoretic strength of our theory—which is intensional in a meaning to be described below—is characterized by the Feferman–Schütte ordinal Γ0. Our approach is similar to the building up of fixed points over state spaces in the propositional modal μ-calculus
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DOI 10.1016/j.apal.2003.11.032
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References found in this work BETA

On the Relationship Between ATR 0 And.Jeremy Avigad - 1996 - Journal of Symbolic Logic 61 (3):768-779.
On the Relationships Between ATR0 and $\Widehat{ID}_{.Jeremy Avigad - 1996 - Journal of Symbolic Logic 61 (3):768 - 779.
Μ-Definable Sets of Integers.Robert S. Lubarsky - 1993 - Journal of Symbolic Logic 58 (1):291-313.

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