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Organizers |
The last forcing standing
by
Andrzej Roslanowski
University of Nebraska at Omaha, Department of Mathematics, Omaha NE68182
Coauthors: Saharon Shelah
In a sequence of previous papers ([RoSh:655], [RoSh:777], [RoSh:860], [RoSh:888] and [RoSh:890]) we introduced several properties of forcing notions guaranteeing that their l-support iterations a proper (for an uncountable cardinal l). Several forcing notions built according to a scheme somewhat similar to forcings with tress and creatures were covered by those properties, however one example of interest to us was not included. In the talk we will introduce a property and an iteration theorem showing that for an inaccessible cardinal l, one may succesfully iterate with l-support the following forcing notion Ql:
Conditions in Ql are complete perfect trees T ⊆ < ll in which every splitting is to a club of l and the limit of an increasing sequence of splitting nodes is a spliting node. The order is the inclusion.
Date received: July 21, 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 # caxi-52.