Journal of Philosophical Logic 42 (5):679-695 (2013)

Abstract
We investigate what happens when ‘truth’ is replaced with ‘provability’ in Yablo’s paradox. By diagonalization, appropriate sequences of sentences can be constructed. Such sequences contain no sentence decided by the background consistent and sufficiently strong arithmetical theory. If the provability predicate satisfies the derivability conditions, each such sentence is provably equivalent to the consistency statement and to the Gödel sentence. Thus each two such sentences are provably equivalent to each other. The same holds for the arithmetization of the existential Yablo paradox. We also look at a formulation which employs Rosser’s provability predicate
Keywords Incompleteness  Omega-liar  Yablo’s paradox  Paradox  Provability  Arithmetic  Goedel
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DOI 10.1007/s10992-012-9244-4
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References found in this work BETA

Paradox Without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251.
An Introduction to Gödel's Theorems.Peter Smith - 2007 - Cambridge University Press.
Yablo’s Paradox.Graham Priest - 1997 - Analysis 57 (4):236–242.
Yablo's Paradox.Graham Priest - 1997 - Analysis 57 (4):236-242.

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Citations of this work BETA

Yablifying the Rosser Sentence.Graham Leach-Krouse - 2014 - Journal of Philosophical Logic 43 (5):827-834.
Liar-Type Paradoxes and the Incompleteness Phenomena.Makoto Kikuchi & Taishi Kurahashi - 2016 - Journal of Philosophical Logic 45 (4):381-398.
Rosser-Type Undecidable Sentences Based on Yablo’s Paradox.Taishi Kurahashi - 2014 - Journal of Philosophical Logic 43 (5):999-1017.
Buttresses of the Turing Barrier.Paolo Cotogno - 2015 - Acta Analytica 30 (3):275-282.

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