The Journal of Symbolic Logic

Research Article

Forcing and stable ordered–union ultrafilters

Todd Eisworth

Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, E-mail: eisworth@math.uni.edu, URL: http://www.math.uni.edu/~eisworth

Abstract

We investigate the effect of a variant of Matet forcing on ultrafilters in the ground model and give a characterization of those P–points that survive such forcing, answering a question left open by Blass [4]. We investigate the question of when this variant of Matet forcing can be used to diagonalize small filters without destroying P–points in the ground model. We also deal with the question of generic existence of stable ordered-union ultrafilters.

(Received September 21 1998)

(Revised April 06 2001)

Key words and phrases

  • ordered–union ultrafilters;
  • Matet forcing;
  • Hindman's Theorem;
  • cardinal characteristics