Classifying First Order Theories by Borel Reducibility - Status Report

Explore the Borel complexity of classes of countable models of first-order theories in this 58-minute mathematical lecture. Discover the fundamental differences between analyzing countable and uncountable models, requiring the development of specialized tools and methodologies. Learn about key techniques including potential canonical Scott sentences, groundedness, flat structures, and the admission of nested sequences. Examine various examples, including some unexpected cases, while engaging with numerous open problems in this active area of research. Gain insights into collaborative work with Danielle Ulrich that advances our understanding of how first-order theories can be classified through Borel reducibility methods.