Vive la difference III

Abstract

We show that, consistently, there is an ultrafilter F on omega such that if N^l_n=(P^l_n cup Q^l_n,P^l_n,Q^l_n,R^l_n) (for l =1,2, n< omega), P^l_n cup Q^l_n subseteq omega, and prod_{n<omega} N^1_n/F and prod_{n< omega}N^2_n/F are isomorphic models of the canonical theory t^ind of the strong independence property, then every isomorphism from prod_{n<omega} N^1_n/F onto prod_{n<omega} N^2_n/F is a product isomorphism.