Logic Seminar-Effective Ultrapowers of Function Structures

Time: Thursday, October 13, 11:00 am-12:00 noon

Place: Smith 120

Speaker:  Keshav Srinivasan, GWU

Title: Effective Ultrapowers of Function Structures

Abstract: We consider a computability-theoretic product construction for structures. We start with a computable structure and consider partial computable sequences modulo a fixed cohesive set. A cohesive set is an infinite set of natural numbers that cannot be split into two infinite subsets by any computably enumerable set.  We focus on structures with a single unary function satisfying various conditions. Unlike most classical ultrapowers, cohesive powers are countable structures and can be isomorphic to the original structure. We investigate the isomorphism types of cohesive powers, as well as their properties when they are not isomorphic to the original structure.