Titlebook: Gentzen‘s Centenary; The Quest for Consis Reinhard Kahle,Michael Rathjen Book 2015 Springer International Publishing Switzerland 2015 Consi

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Book 2015e-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in computer science such as automated theorem proving and type theory.   .

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https://doi.org/10.1007/978-3-642-93604-3t. In a letter to Bernays dated November 4, 1935, Gentzen protested this evaluation; but then, in another letter to him dated December 11, 1935, he admits that the ‘critical inference in my consistency proof is defective’.

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https://doi.org/10.1007/978-3-642-91399-0In this article we study subsystems .. of the theory .. in which fixed point induction is restricted to properly stratified formulas.