Logic Seminar

Rachael Alvir, Department of Pure Mathematics, University of Waterloo

"Scott Complexity"

Scott's Isomorphism Theorem states that every countable structure can be described up to isomorphism (among countable structures) by a single sentence of $L_{\omega_1 \omega}$ known as its Scott sentence. Here, $L_{\omega_1 \omega}$ is the extension of finitary first-order logic obtained by allowing countably infinite conjunctions and disjunctions. Each structure has a least complexity Scott sentence in the hierarchy of $\Pi_{\alpha}, \Sigma_{\alpha},$ and $d$-$\Sigma_\alpha$ formulas known as its Scott complexity. In this talk, we compute the Scott complexity of several kinds of linear orders and groups.

MC 5479