Rosser-Type Undecidable Sentences Based on Yablo’s Paradox

Journal of Philosophical Logic 43 (5):999-1017 (2014)

Abstract
It is widely considered that Gödel’s and Rosser’s proofs of the incompleteness theorems are related to the Liar Paradox. Yablo’s paradox, a Liar-like paradox without self-reference, can also be used to prove Gödel’s first and second incompleteness theorems. We show that the situation with the formalization of Yablo’s paradox using Rosser’s provability predicate is different from that of Rosser’s proof. Namely, by using the technique of Guaspari and Solovay, we prove that the undecidability of each instance of Rosser-type formalizations of Yablo’s paradox for each consistent but not Σ1-sound theory is dependent on the choice of a standard proof predicate
Keywords Incompleteness theorems  Yablo’s paradox  Rosser’s provability predicates  Proof predicates  Guaspari-Solovay’s construction
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DOI 10.1007/s10992-013-9309-z
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References found in this work BETA

Paradox Without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251.
The Logic of Provability.George S. Boolos - 1993 - Cambridge University Press.
Yablo’s Paradox.Graham Priest - 1997 - Analysis 57 (4):236–242.
Gödelizing the Yablo Sequence.Cezary Cieśliński & Rafal Urbaniak - 2013 - Journal of Philosophical Logic 42 (5):679-695.

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Citations of this work BETA

Liar-Type Paradoxes and the Incompleteness Phenomena.Makoto Kikuchi & Taishi Kurahashi - 2016 - Journal of Philosophical Logic 45 (4):381-398.
On Rosser's Provability Predicates.Taishi Kurahashi - 2014 - Journal of the Japan Association for Philosophy of Science 41 (2):93-101.

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