Gödel's reformulation of Gentzen's first consistency proof for arithmetic: the no-counterexample interpretation

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.