Joost Joosten
Universitat de Barcelona

Abstract: Iteratively adding reflection principles or consistency statements to a weak base theory yields a paradigm for ordinal analysis: how often should we iterate to adequately approach a target theory? We revisit some basic early results obtained by Schmerl and then expose Beklemishev's uniform approach to computing these proof theoretical ordinals using provability logics. Towards the end of the talk we discuss the current state of the art looking at fragments of second order arithmetic and weak fragments of set theory.

This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.