Various points in the space of uniform ultrafilters
by
Joni E. Baker
University of Wisconsin

Let u(\kappa) be the space of uniform ultrafilters over the infinite cardinal \kappa. We say that the point x is a weak P_\kappa⁺ -point in the space X iff x is not an accumulation point of any subset of X \{x} of size \kappa or less. Then a weak P-point is just a weak P_\omega1-point. Kunen (1980) proved that there is a weak P-point in u(\omega) = \omega^*; then, Baker, Kunen (2000) showed that when \kappa is regular, this result generalizes; i.e., there is a weak P_\kappa⁺ -point in u(\kappa). (This point is also good, in the sense of Keisler.)

Here, we will discuss some other results along these lines. In particular, for regular \kappa, one can find a set of weak P_\kappa⁺ -points of u(\kappa), which is of size \kappa⁺ and which is dense in itself.

Date received: May 11, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagw-25.