New reals: Can live with them, can live without them
arXiv:math/0505471 · doi:10.1002/malq.200510018
Abstract
We give a self-contained proof of the preservation theorem for proper countable support iterations known as "tools-preservation," "Case A" or "first preservation theorem" in the literature. We do not assume that the forcings add reals.
(an incorrect claim following Fact 2.3 was removed)