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 $\leq$ min. 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].