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- W171610189 abstract "A central theme running through all the main areas of Mathematical Logic is the classification of sets, functions or theories, by means of transfinite hierarchies whose ordinal levels measure their ‘rank’ or ‘complexity’ in some sense appropriate to the underlying context. In Proof Theory this is manifest in the assignment of ‘proof theoretic ordinals’ to theories, gauging their ‘consistency strength’ and ‘computational power’. Ordinal-theoretic proof theory came into existence in 1936, springing forth from Gentzen’s head in the course of his consistency proof of arithmetic. To put it roughly, ordinal analyses attach ordinals in a given representation system to formal theories. Though this area of mathematical logic has is roots in Hilbert’s “Beweistheorie” the aim of which was to lay to rest all worries about the foundations of mathematics once and for all by securing mathematics via an absolute proof of consistency technical results in proof theory are not different from those in any other branch of mathematics, inasmuch as they can be understood in a way that does not at all refer to any kind of (modified) Hilbert programme. In actuality, most proof theorists do not consider themselves pursuing consistency proofs. The present paper is based on the lectures that I gave at the LC ’97. The lectures were an attempt to give an overview of results that have been achieved by means of ordinal analyses, and to explain the current rationale and goals of ordinally informative" @default.
- W171610189 created "2016-06-24" @default.
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- W171610189 date "2007-01-01" @default.
- W171610189 modified "2023-09-26" @default.
- W171610189 title "The Realm of Ordinal Analysis" @default.
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