Graduate Student Seminar-Cohesive Powers of Structures

Date and Time: Tuesday, February 8, 1-2pm

Place: Zoom
Zoom link:https://gwu-edu.zoom.us/j/92957649236?pwd=YmZIYytSUVVwcU1RdjZHYkNFak10U…

Speaker:  Keshav Srinivasan, GWU

Title: Cohesive Powers of Structures

Abstract:While typical ultrapower constructions in mathematical logic produce uncountable models, cohesive power constructions allow us to algorithmically build countable non-standard models with interesting properties. I will explain how cohesive powers work, and outline recent research I've done on cohesive powers for structures from various important classes of directed graphs. I will state 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.  I will outline a classification of certain structures from concrete classes when the cohesive power is isomorphic to the original structure.