Ordinal Analysis of Weak Theories Part 2

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

In the second of two talks 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.