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Cohen reals from small forcings
Published online by Cambridge University Press: 12 March 2014
Abstract
We introduce a new cardinal characteristic r*. related to the reaping number r. and show that
• posets of size < r* which add reals add unbounded reals;
• posets of size < r which add unbounded reals add Cohen reals.
We also show that add() ≤ min(r. r*). It follows that posets of size < add() which add reals add Cohen reals.
This improves results of Roslanowski and Shelah [RS] and of Zapletal [Z].
- Type
- Research Article
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- Copyright © Association for Symbolic Logic 2001