# Computability Learning Seminar

Thursday, September 22, 2022 — 10:30 AM EDT

Rachael Alvir, Department of Pure Mathematics, University of Waterloo

"Scott Complexity"

The logic $L_{\omega_1} \omega$ is the extension of finitary first-order logic which allows for infinite conjunctions and disjunctions. Scott's isomorphism theorem states that every countable structure can be described up to isomorphism by a single sentence of  $L_{\omega_1} \omega$ known as its Scott sentence. There is an important invariant of a countable structure, related to its Scott sentence, known as its Scott rank. Unfortunately, many non-equivalent definitions of Scott rank existed in the literature. In this talk we discuss Scott complexity, the least complexity of a Scott sentence for the structure, and argue for why it should be the standard invariant studied in favor of Scott rank.

MC 5417

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