Gödel's reformulation of Gentzen's first consistency proof for arithmetic: The no-counterexample interpretation
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Bulletin of Symbolic Logic 11 (2):225-238 (2005)
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 P A , 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 Godel's reformulation, and discuss the relation between the two proofs.
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Charles Parsons (2009). William Tait. The Provenance of Pure Reason. Essays on the Philosophy of Mathematics and on its History. Philosophia Mathematica 17 (2):220-247.
Julien Boyer & Gabriel Sandu (2012). Erratum To: Between Proof and Truth. Synthese 187 (3):973-974.
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