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Cohen reals from small forcings

Published online by Cambridge University Press:  12 March 2014

Janusz Pawlikowski
Janusz Pawlikowski*
Affiliation:
Department of Mathematics, University of Wroclaw, PL. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
*
Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, USA, E-mail: pawlikow@math.uni.wroc.pl
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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
Information
The Journal of Symbolic Logic , Volume 66 , Issue 1 , March 2001 , pp. 318 - 324
Copyright
Copyright © Association for Symbolic Logic 2001

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References

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