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 firstorder 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