SELF-REFERENCE IN ARITHMETIC I

@article{Halbach2014SELFREFERENCEIA,
  title={SELF-REFERENCE IN ARITHMETIC I},
  author={Volker Halbach and Albert Visser},
  journal={The Review of Symbolic Logic},
  year={2014},
  volume={7},
  pages={671 - 691}
}
Abstract A Gödel sentence is often described as a sentence saying about itself that it is not provable, and a Henkin sentence as a sentence stating its own provability. We discuss what it could mean for a sentence of arithmetic to ascribe to itself a property such as provability or unprovability. The starting point will be the answer Kreisel gave to Henkin’s problem. We describe how the properties of the supposedly self-referential sentences depend on the chosen coding, the formulae expressing… 

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