## Journal of Symbolic Logic

### Cohen Reals from Small Forcings

Janusz Pawlikowski

#### 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($\mathscr{M}$) $\leq$ min(r, r*). It follows that posets of size < add($\mathscr{M}$) which add reals add Cohen reals. This improves results of Roslanowski and Shelah [RS] and of Zapletal [Z].

#### Article information

Source
J. Symbolic Logic, Volume 66, Issue 1 (2001), 318-324.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183746373

Mathematical Reviews number (MathSciNet)
MR1825187

Zentralblatt MATH identifier
0980.03054

JSTOR