On the Elementary Theory of Graph Products of Groups

Explore the model theory of groups through this 59-minute conference talk examining which group-theoretic constructions preserve elementary theory. Begin with Feferman and Vaught's 1959 findings on direct products showing that direct products of elementarily equivalent groups remain elementarily equivalent, then contrast this with Sela's recent 2017 solution to the long-standing conjecture about invariance of elementary equivalence under free products. Address the converse question of when factors are elementarily equivalent given two elementary equivalent free products of groups or more generally graph products of groups. Discover sufficient conditions for this equivalence and apply these results to describe finitely generated groups that are elementarily equivalent to Right-Angled Artin Groups (RAAGs) whose underlying graph forms a transitive forest. Gain insights into advanced topics in mathematical logic, group theory, and model theory through this specialized mathematical presentation from the Hausdorff Center for Mathematics.