
Organizers 
Properties of Cohesive Powers
by
Rumen Dimitrov
Department of Mathematics, Western Illinois University, Macomb IL 61455
The cohesive sets are infinite sets that cannot be split into two infinite subsets by computably enumerable sets. Each cohesive set can be used to define an ultrafilter in the Boolean algebra of computable sets. We will introduce the notion of cohesive power ∏_{C}\QTRcalA of a computable structure \QTRcalA over a cohesive set C. We will give examples of algebraic structures \QTRcalA such that \QTRcalA and ∏_{C}\QTRcalA are isomorphic as well as when \QTRcalA and ∏_{C}\QTRcalA do not satisfy the same first order formulas. We will discuss the question of isomorphisms of ∏_{C1}\QTRcalA and ∏_{C2}\QTRcalA when C_{1} and C_{2} are cohesive.
Date received: December 19, 2013
Copyright © 2013 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbid15.