General (Main) Seminar MSRI program on DDC-Effective ultrapowers

General (Main) Seminar MSRI program on DDC

Organizer: A. Shlapentokh

For link contact harizanvgwu [dot] edu

Friday, October 9, 12:00-1:00 on Zoom

Speaker:  Valentina Harizanov, GWU

Title: Effective ultrapowers

Abstract: Effective ultrapowers of structures are computability-theoretic analogs of ultrapowers. We assume that the structures are computable; that is, they have computable domains and decidable atomic diagrams. The role of an ultrafilter is played by an infinite set of natural numbers that is indecomposable into two infinite parts by computably enumerable (i.e., Diophantine) sets. Such indecomposable sets can even have computably enumerable complements. Effective ultrapower construction allows us to build countable non-standard models with interesting properties. Recent work that focuses on effective ultrapowers of the ordered set of natural numbers is joint with R. Dimitrov, A. Morozov, P. Shafer, A. Soskova and S. Vatev. The lecture will require no background in computability theory.