Well-ordering principles and the reverse mathematics zoo

Abstract: Over the moderately strong base theory ACA$_0$ from reverse mathematics, any $\Pi^1_2$-statement corresponds to a transformations of well-orders (i.e., to a dilator). We will show that, in contrast, there is a dichotomy over the weaker base theory RCA$_0$. Here, transformations of well-orders are either weak or have a certain minimal strength. It follows that $\Pi^1_2$-statements in a certain gap cannot correspond to a transformation of well-orders. Ramsey's theorem for pairs is a particularly prominent $\Pi^1_2$-statement in this gap. The talk is based on https://doi.org/10.1142/S0219061325500102. It is directed at a general logical audience.

logic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic