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Spring Topology and Dynamical Systems Conference 2008
March 13-15, 2008
University of Wisconsin Milwaukee and Marquette University
Milwaukee, WI, USA

Organizers
Ric Ancel, Karen Brucks, Craig Guilbault, Chris Hruska, Suzanne Hruska, Boris Okun (UWM); Paul Bankston (Marquette); Lois Kailhofer (Alverno College).

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Diamond and ultrafilters
by
David Milovich
University of Wisconsin-Madison

Two directed sets are said to be Tukey equivalent if they order-embed as cofinal subsets of a common directed set. John Isbell (in 1965) asked if all nonprincipal ultrafilters on omega, ordered by containment, are Tukey equivalent. The main result I will present is that Diamond implies the answer is negative. (Diamond can here be weakened to MA+not(CH)+Diamond(S) for an appropriate S. Open: does CH suffice?) I will also present results about Tukey classes of ultrafilters ordered by almost containment.

Date received: February 26, 2008

Copyright © 2008 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 # cawk-82.