23-25 January, Universidade do Minho, Braga, Portugal

Michael Rathjen (University of Leeds, U.K.)

Proof Theory: From arithmetic to set theory

Abstract: Ordinal analysis of theories is a core area of proof theory. The origins of proof theory can be traced back to the second problem on Hilbert's famous list of problems. Proof theory was invented as the main tool for carrying out Hilbert's programme. In the main, ordinal-theoretic proof theory came into existence in 1936, springing forth from Gentzen's consistency proof of arithmetic. The intent of the talks is to elucidate the underlying notions, the ubiquitous tool of cut elimination and the rationale of ordinal-theoretic proof theory by relating the developments from Gentzen up to more recent advances in ordinal analysis of set theories.