Gödelizing the Yablo sequence

TitleGödelizing the Yablo sequence
Publication TypeJournal Article
Year of Publication2013
AuthorsCieśliński, C, Urbaniak, R
JournalJournal of philosophical logic

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 Godel 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.

Citation Key4443766