Logic Seminar- Cohesive powers of directed graphs

Thu, 14 October, 2021 8:30pm

Time: Thursday, October 14, 4:30-5:30PM

Place: zoom


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.

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