A generalization of the Second Incompleteness Theorem and some exceptions to it

Annals of Pure and Applied Logic 141 (3):472-496 (2006)
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Abstract

This paper will introduce the notion of a naming convention and use this paradigm to both develop a new version of the Second Incompleteness Theorem and to describe when an axiom system can partially evade the Second Incompleteness Theorem

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10.1016/j.apal.2005.12.010

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Citations of this work

Current Research on Gödel’s Incompleteness Theorems.Yong Cheng - 2021 - Bulletin of Symbolic Logic 27 (2):113-167.
Passive induction and a solution to a Paris–Wilkie open question.Dan E. Willard - 2007 - Annals of Pure and Applied Logic 146 (2-3):124-149.
On the Depth of Gödel’s Incompleteness Theorems.Yong Cheng - forthcoming - Philosophia Mathematica.

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References found in this work

On notation for ordinal numbers.S. C. Kleene - 1938 - Journal of Symbolic Logic 3 (4):150-155.
On the scheme of induction for bounded arithmetic formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (C):261-302.
Existence and feasibility in arithmetic.Rohit Parikh - 1971 - Journal of Symbolic Logic 36 (3):494-508.
Extensions of some theorems of gödel and church.Barkley Rosser - 1936 - Journal of Symbolic Logic 1 (3):87-91.

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