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Another look at the second incompleteness theorem
Review of Symbolic Logic 13 (2):269-295 (2020)
Abstract
In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is fixed and the representation of the set of axioms varies. We extend the Feferman framework in one important point: we allow the interpretation of number theory to vary.Author's Profile
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Citations of this work
There May Be Many Arithmetical Gödel Sentences.Kaave Lajevardi & Saeed Salehi - 2021 - Philosophia Mathematica 29 (2):278–287.
Current Research on Gödel’s Incompleteness Theorems.Yong Cheng - 2021 - Bulletin of Symbolic Logic 27 (2):113-167.
Gödel’s Second Incompleteness Theorem: How It is Derived and What It Delivers.Saeed Salehi - 2020 - Bulletin of Symbolic Logic 26 (3-4):241-256.
The absorption law: Or: how to Kreisel a Hilbert–Bernays–Löb.Albert Visser - 2020 - Archive for Mathematical Logic 60 (3-4):441-468.
References found in this work
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Cuts, consistency statements and interpretations.Pavel Pudlák - 1985 - Journal of Symbolic Logic 50 (2):423-441.
Notes on polynomially bounded arithmetic.Domenico Zambella - 1996 - Journal of Symbolic Logic 61 (3):942-966.
An Inside View of Exp; or, The Closed Fragment of the Provability Logic of IΔ0+ Ω1 with a Propositional Constant for.Albert Visser - 1992 - Journal of Symbolic Logic 57 (1):131-165.
Arithmetical Completeness Theorem for Modal Logic $$mathsf{}$$.Taishi Kurahashi - 2018 - Studia Logica 106 (2):219-235.
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