{'fraction_non_alphanumeric': 0.048736462093862815, 'fraction_numerical': 0.005415162454873646, 'mean_word_length': 5.607142857142857, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
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.