Bulletin of Symbolic Logic 11 (2):225-238 (2005)

William W. Tait
University of Chicago
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 [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 Godel's reformulation, and discuss the relation between the two proofs.
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DOI 10.2178/bsl/1120231632
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References found in this work BETA

On the Interpretation of Non-Finitist Proofs—Part I.G. Kreisel - 1951 - Journal of Symbolic Logic 16 (4):241-267.
A Semantics of Evidence for Classical Arithmetic.Thierry Coquand - 1995 - Journal of Symbolic Logic 60 (1):325-337.
Functionals Defined by Transfinite Recursion.W. W. Tait - 1965 - Journal of Symbolic Logic 30 (2):155-174.
The Substitution Method.W. W. Tait - 1965 - Journal of Symbolic Logic 30 (2):175-192.
Update Procedures and the 1-Consistency of Arithmetic.Jeremy Avigad - 2002 - Mathematical Logic Quarterly 48 (1):3-13.

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Citations of this work BETA

Hilbert's Program Then and Now.Richard Zach - 2007 - In Dale Jacquette (ed.), Philosophy of Logic. Amsterdam: North Holland. pp. 411–447.
Reading Gentzen's Three Consistency Proofs Uniformly.Ryota Akiyoshi & Yuta Takahashi - 2013 - Journal of the Japan Association for Philosophy of Science 41 (1):1-22.

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