Paweł Parys

A Dichotomy Theorem for Ordinal Ranks in MSO

We focus on formulae $\exists X.\, φ(\vec{Y}, X)$ of monadic second-order logic over the full binary tree, such that the witness $X$ is a well-founded set. The ordinal rank $\mathrm{rank}(X) < ω_1$ of such a set $X$ measures its depth and branching structure. We search for the le...