Gödelizing the Yablo Sequence

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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C. Cieslinski (2002). Heterologicality and Incompleteness. Mathematical Logic Quarterly 48 (1):105-110.

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