Oberseminar "Mathematische Logik" - Prof. Dr. Anton Freund

Many important principle are unprovable over the base theory RCA₀ of reverse mathematics but conservative over the latter. For example, while RCA₀ cannot prove the infinite pigeonhole principle PHP, any Pi⁰₃-consequence of PHP is provable in RCA₀. In this talk, I present a general result to the effect that a principle P is Pi⁰₃-conservative over RCA₀ precisely when RCA₀ proves certain approximations P_n for each n. This result is shown by proof-theoretic methods, which are rather different from the known forcing and indicator arguments. To illustrate how the result can be used, I give a new proof of the well-known fact that PHP is Pi⁰₃-conservative over RCA₀. The talk is based on joint work with Gabriele Buriola, Giacomo Cozzi and Antonia Dammrau.