University Seminar- Computability, Complexity, and Algebraic Structure

Time: Wednesday, November 8, 11:15am – 12:15pm

Place: Monroe Hall, Room 250

Speaker: Valentina Harizanov, GWU

Title:  Cohesive products of structures

Abstract: A cohesive product of a sequence of structures is an effective analog of an ultraproduct, where the structures are uniformly computable, and a cohesive set of natural numbers plays the role of an ultrafilter. Instead of building a structure from all functions, we build a structure from only partial computable functions. Thus, the cohesive product construction allows us to effectively obtain countable models with interesting properties. Here, Dimitrov’s theorem for cohesive powers is a restricted version of the classical  Łoś’s theorem, but additional decidability on the structures plays a significant role in satisfiability of more complicated formulas in the product.