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Friedberg Numbering in Fragments of Peano Arithmetic and α-Recursion Theory
Published online by Cambridge University Press: 12 March 2014
Abstract
In this paper, we investigate the existence of a Friedberg numbering in fragments of Peano Arithmetic and initial segments of Gödel's constructible hierarchy Lα, where α is Σ1 admissible. We prove that
(1) Over P− + BΣ2, the existence of a Friedberg numbering is equivalent to IΣ2, and
(2) For Lα, there is a Friedberg numbering if and only if the tame Σ2 projectum of α equals the Σ2 cofinality of α.
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- Research Article
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- Copyright © Association for Symbolic Logic 2013
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