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

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Semi-Formal Calculi and Their Applicationses was already suggested by David Hilbert in his paper “Die Grundlegung der elementaren Zahlentheorie” [6] and was later systematically used by Kurt Schütte in his work on proof theory. The heigths of proof trees in a semi-formal system are canonically measured by ordinals. Therefore, in contrast to

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https://doi.org/10.1007/978-3-642-50901-8tamathematical investigations. We investigate three approaches for trustworthy principles, namely ordinal notation systems built from below, Martin-Löf type theory, and Feferman’s system of explicit mathematics. We will review what is known about the strength up to which direct validation can be pro

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https://doi.org/10.1007/978-3-322-98670-2the same vein we also wonder whether the search for strictly mathematical examples of an incompleteness in . really attained its “holy grail” status before the late 1970s. Almost no direct moral is ever given; rather, the paper strives to lay out evidence for the reader to consider and have the read