Gödel's Reformulation of Gentzen's First Consistency Proof For Arithmetic: The No-Counterexample Interpretation

@article{Tait2005GdelsRO,
  title={G{\"o}del's Reformulation of Gentzen's First Consistency Proof For Arithmetic: The No-Counterexample Interpretation},
  author={William W. Tait},
  journal={Bulletin of Symbolic Logic},
  year={2005},
  volume={11},
  pages={225 - 238}
}
  • W. Tait
  • Published 1 June 2005
  • Mathematics, Philosophy
  • Bulletin of Symbolic Logic
Abstract The last section of “Lecture at Zilsel's” [9, §4] contains an interesting but quite condensed discussion of Gentzen's first version of his consistency proof for PA [8], reformulating it as what has come to be called the no-counterexample interpretation. I will describe Gentzen's result (in game-theoretic terms), fill in the details (with some corrections) of Gödel's reformulation, and discuss the relation between the two proofs. 
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