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II Workshop on Coverings, Selections and Games in Topology
December 19-22, 2005
University of Lecce
Lecce, Italy

Organizers
(Organizing Committee) Cosimo Guido, Anna Frascella, Domenico Lenzi, Gabriella Zammillo. (Scientific Committee) Liljana Babinkostova, Cosimo Guido, Ljubisa Kocinac, Marion Scheepers, Boaz Tsaban

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On the number of near-coherence classes
by
Heike Mildenberger
University of Vienna, Kurt Goedel Research Center for Mathematical Logic

We show that if the number of near-coherence classes of ultrafilters is larger than (1 + the number of cardinals in [max(b, gf), u]), then it is infinite. Thus we give a partial answer to a question by Banakh and Blass. It is open whether max(b, gf) < u < d is consistent relative to ZFC. We show that in the models of u < d from Blass and Shelah there are 2c near-coherence classes, thus answering another question by Banakh and Blass. By an unpublished result of Canjar, there are at least two classes in these models. gf is the groupwise density number for filters and gf is at least g.

Date received: November 4, 2005

Copyright © 2005 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 # caqh-19.