The non-constructive μ operator, fixed point theories with ordinals, and the bar rule

Annals of Pure and Applied Logic 104 (1-3):305-324 (2000)
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Abstract

This paper deals with the proof theory of first-order applicative theories with non-constructive μ operator and a form of the bar rule, yielding systems of ordinal strength Γ0 and 20, respectively. Relevant use is made of fixed-point theories with ordinals plus bar rule

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Unfolding finitist arithmetic.Solomon Feferman & Thomas Strahm - 2010 - Review of Symbolic Logic 3 (4):665-689.
Universes over Frege structures.Reinhard Kahle - 2003 - Annals of Pure and Applied Logic 119 (1-3):191-223.

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