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Gödelizing the Yablo sequence

(2013) JOURNAL OF PHILOSOPHICAL LOGIC. 42(5). p.679-695
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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 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.
Keywords
meta-arithmetic, PARADOX, arithmetic, logic, incompleteness, Yablo paradox, paradox

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Please use this url to cite or link to this publication:

MLA
Cieśliński, Cezary, and Rafal Urbaniak. “Gödelizing the Yablo Sequence.” JOURNAL OF PHILOSOPHICAL LOGIC 42.5 (2013): 679–695. Print.
APA
Cieśliński, C., & Urbaniak, R. (2013). Gödelizing the Yablo sequence. JOURNAL OF PHILOSOPHICAL LOGIC, 42(5), 679–695.
Chicago author-date
Cieśliński, Cezary, and Rafal Urbaniak. 2013. “Gödelizing the Yablo Sequence.” Journal of Philosophical Logic 42 (5): 679–695.
Chicago author-date (all authors)
Cieśliński, Cezary, and Rafal Urbaniak. 2013. “Gödelizing the Yablo Sequence.” Journal of Philosophical Logic 42 (5): 679–695.
Vancouver
1.
Cieśliński C, Urbaniak R. Gödelizing the Yablo sequence. JOURNAL OF PHILOSOPHICAL LOGIC. 2013;42(5):679–95.
IEEE
[1]
C. Cieśliński and R. Urbaniak, “Gödelizing the Yablo sequence,” JOURNAL OF PHILOSOPHICAL LOGIC, vol. 42, no. 5, pp. 679–695, 2013.
@article{4443766,
  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 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.},
  author       = {Cieśliński, Cezary and Urbaniak, Rafal},
  issn         = {0022-3611},
  journal      = {JOURNAL OF PHILOSOPHICAL LOGIC},
  keywords     = {meta-arithmetic,PARADOX,arithmetic,logic,incompleteness,Yablo paradox,paradox},
  language     = {eng},
  number       = {5},
  pages        = {679--695},
  title        = {Gödelizing the Yablo sequence},
  url          = {http://dx.doi.org/10.1007/s10992-012-9244-4},
  volume       = {42},
  year         = {2013},
}

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