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Friedberg Numbering in Fragments of Peano Arithmetic and α-Recursion Theory

Published online by Cambridge University Press:  12 March 2014

Wei Li
Wei Li*
Affiliation:
Department of Mathematics, National University of Singapore, 119076, Singapore, E-mail: wei.li@nus.edu.sg
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 4 , December 2013 , pp. 1135 - 1163
Copyright
Copyright © Association for Symbolic Logic 2013

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