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December 2013 Friedberg numbering in fragments of Peano Arithmetic and $\alpha$-recursion theory
Wei Li
J. Symbolic Logic 78(4): 1135-1163 (December 2013). DOI: 10.2178/jsl.7804060

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 $L_\alpha$, where $\alpha$ is $\Sigma_1$ admissible. We prove that

(1) Over $P^-+B\Sigma_2$, the existence of a Friedberg numbering is equivalent to $I\Sigma_2$, and

(2) For $L_\alpha$, there is a Friedberg numbering if and only if the tame $\Sigma_2$ projectum of $\alpha$ equals the $\Sigma_2$ cofinality of $\alpha$.

Citation

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Wei Li. "Friedberg numbering in fragments of Peano Arithmetic and $\alpha$-recursion theory." J. Symbolic Logic 78 (4) 1135 - 1163, December 2013. https://doi.org/10.2178/jsl.7804060

Information

Published: December 2013
First available in Project Euclid: 5 January 2014

zbMATH: 1349.03084
MathSciNet: MR3156515
Digital Object Identifier: 10.2178/jsl.7804060

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 4 • December 2013
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