Cofinalities of countable ultraproducts: The existence theorem

Abstract

We show that there exists an ultrafilter U in the set IN of natural numbers such that the cofinality of the iZ-ultrapower n1N/U equals cof(of), where d is the minimal cardinality of a dominating subfamily of NIN. Moreover, the coinitiality of the family of finite-to-one functions in this ultrapower is also cof(i/). If c = d, then U may be taken to be a P-point. © 1989 by the University of Notre Dame. All rights reserved.