Logic Seminar

Tuesday, February 14, 2023 2:30 pm - 2:30 pm EST (GMT -05:00)

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