# Ordinal Analysis of Weak Theories

**Date**: Wednesday 20 March 2019, 14:00 – 15:00**Location**: Mathematics Level 8, MALL 1, School of Mathematics**Type**: Proofs, Constructions and Computations, Seminars, Pure Mathematics**Cost**: Free

#### Michael Rathjen, University of Leeds. Part of the proofs, constructions and computations seminar series.

We fill an apparent gap in the literature by giving a short and self-contained proof that the ordinal of the theory RCA_0 + WO(\sigma) is \sigma^\omega, for any ordinal \sigma satisfying \omega \cdot \sigma = \sigma (e.g., \omega^\omega, \omega^{\omega^\omega}, \varepsilon_0). Theories of the form RCA_0 + WO(\sigma) are of interest in Proof Theory and Reverse Mathematics because of their connections to a number of well-investigated combinatorial principles related to various subsystems of arithmetic.