, Volume 42, Issue 5, pp 679-695,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 01 Sep 2012

Gödelizing the Yablo Sequence

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.

Graham Leach–Krouse cooperated with us in early stages of this work. Other commitments did not allow him to continue. His short note on the subject is available at http://arxiv.org/abs/1110.2056.