Fixed points in Peano arithmetic with ordinals

Annals of Pure and Applied Logic 60 (2):119-132 (1993)
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Abstract

Jäger, G., Fixed points in Peano arithmetic with ordinals, Annals of Pure and Applied Logic 60 119-132. This paper deals with some proof-theoretic aspects of fixed point theories over Peano arithmetic with ordinals. It studies three such theories which differ in the principles which are available for induction on the natural numbers and ordinals. The main result states that there is a natural theory in this framework which is a conservative extension of Peano arithmeti

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10.1016/0168-0072(93)90039-g

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Citations of this work

The unfolding of non-finitist arithmetic.Solomon Feferman & Thomas Strahm - 2000 - Annals of Pure and Applied Logic 104 (1-3):75-96.
On Feferman’s operational set theory OST.Gerhard Jäger - 2007 - Annals of Pure and Applied Logic 150 (1-3):19-39.
Totality in applicative theories.Gerhard Jäger & Thomas Strahm - 1995 - Annals of Pure and Applied Logic 74 (2):105-120.

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References found in this work

Proof theory and ordinal analysis.W. Pohlers - 1991 - Archive for Mathematical Logic 30 (5-6):311-376.
Levels of implication and type free theories of classifications with approximation operator.Andrea Cantini - 1992 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):107-141.
Beweistheorie von KPN.Kurt Schutte & Gerhard Jager - 1983 - Journal of Symbolic Logic 48 (3):879.

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