Lecture Title: Proof Theory: From Arithmetic to Set Theory
Speaker: Prof. Michael Rathjen (University of Leeds, UK)
Date and Time: 13th October 2020, 4pm-6pm Beijing time (9am-11am UK time)
Organizer: School of Philosophy, Wuhan University
Host: Yong Cheng (Wuhan University)
Commentator: Sam Sanders (TU Darmstadt, Germany)
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’. 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. In the main, modern proof theory came into existence in the 1930s, springing forth from Gentzen's work, especially his consistency proofs of arithmetic. The intent of the talk is to introduce the main notions and results of proof theory and to explain the rationale of ordinal-theoretic proof theory, advancing from arithmetic to set theory.
About the speaker:
Prof. Michael Rathjen is one of the leading experts in modern proof theory. His most outstanding achievements belong to ordinal analysis, the most complicated and technically advanced area of the field, where exciting interplay with set theory, recursion theory and model theory comes into place. He also has made significant contributions to constructive set theory, explicit mathematics and Martin-Loef's type theory. M. Rathjen was an editor for the Journal of Symbolic Logic.
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