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2012 Degrees of Relative Provability
Mingzhong Cai
Notre Dame J. Formal Logic 53(4): 479-489 (2012). DOI: 10.1215/00294527-1722710

Abstract

There are many classical connections between the proof-theoretic strength of systems of arithmetic and the provable totality of recursive functions. In this paper we study the provability strength of the totality of recursive functions by investigating the degree structure induced by the relative provability order of recursive algorithms. We prove several results about this proof-theoretic degree structure using recursion-theoretic techniques such as diagonalization and the Recursion Theorem.

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Mingzhong Cai. "Degrees of Relative Provability." Notre Dame J. Formal Logic 53 (4) 479 - 489, 2012. https://doi.org/10.1215/00294527-1722710

Information

Published: 2012
First available in Project Euclid: 8 November 2012

zbMATH: 1269.03043
MathSciNet: MR2995415
Digital Object Identifier: 10.1215/00294527-1722710

Subjects:
Primary: 03D20
Secondary: 03F99

Rights: Copyright © 2012 University of Notre Dame

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