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Colloquium on Topology, Gyula, Hungary
August 9-15, 1998
János Bolyai Mathematical Society
Budapest, Hungary

Organizers
M. Bognár, A. Császár (chairman), J. Gerlits, I. Juhász, E. Makai, G. Moussong, R. Rimányi, L. Soukup, A. Stipsicz, J. Szenthe, A. Szücs (secretary)

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Applications of totally proper forcing
by
Peter J. Nyikos
University of South Carolina, Columbia, SC 29208
Coauthors: Todd Eisworth

A poset is totally proper if it is proper and does not add reals. While the iteration of totally proper forcings need not be totally proper, the use of countable supports insures that any reals added are very tame and do not affect such cardinal numbers as b or even u or i. Many strong results have recently been obtained by the authors even without adding reals. For example, we have obtained the following PFA-like result:

Date received: June 3, 1998

Copyright © 1998 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 # cabc-22.