Time: Thursday, October 14, 4:30-5:30PM
Speaker: Keshav Srinivasan, GWU
Title: Cohesive powers of directed graphs
Abstract: While typical ultrapower constructions produce uncountable models, cohesive power constructions allow us to algorithmically build countable non-standard models with interesting properties. We will present some of our recent results on cohesive powers for structures from various important classes of directed graphs. We will prove a universal embeddability result for graphs in cohesive powers of strongly locally finite graphs. In general, by Dimitrov's theorem, only first-order properties expressed by sentences at lower levels of arithmetical hierarchy are preserved by cohesive powers. We will outline a classification of certain structures from concrete classes when the cohesive power is isomorphic to the original structure.