There May Be Many Arithmetical Gödel Sentences

Philosophia Mathematica 29 (2):278–287 (2021)
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Abstract

We argue that, under the usual assumptions for sufficiently strong arithmetical theories that are subject to Gödel’s First Incompleteness Theorem, one cannot, without impropriety, talk about *the* Gödel sentence of the theory. The reason is that, without violating the requirements of Gödel’s theorem, there could be a true sentence and a false one each of which is provably equivalent to its own unprovability in the theory if the theory is unsound.

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References found in this work

An Introduction to Gödel's Theorems.Peter Smith - 2007 - New York: Cambridge University Press.
The incompleteness theorems.Craig Smorynski - 1977 - In Jon Barwise (ed.), Handbook of mathematical logic. New York: North-Holland. pp. 821 -- 865.
Arithmetization of Metamathematics in a General Setting.Solomon Feferman - 1960 - Journal of Symbolic Logic 31 (2):269-270.
An Introduction to Gödel's Theorems.Peter Smith - 2009 - Bulletin of Symbolic Logic 15 (2):218-222.

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