Cohen reals from small forcings
by
Janusz Pawlikowski
University of West Virginia

A countable atomless poset adds, of course, a Cohen real. The bigger the poset the more difficult it is to guarantee that it adds Cohen reals. Ros anowski and Shelah and showed that \sigma-linked posets of size < p add Cohen reals. Zapletal weakened `\sigma-linked' to `adding reals'. We improve this result by enlarging p to add(meager): posets of size < add(meager) that add reals add Cohen reals. Roslanowski and Shelah also showed that posets of size < cov(meager) that add unbounded reals add Cohen reals. We show that cov(meager) can be enlarged to the reaping number r. We also introduce a new cardinal characteristic r^* and show that posets of size < r^* which add reals add unbounded reals.

Date received: November 11, 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 # cabr-23.