Specializing Wide Aronszajn Trees without Adding Reals

Abstract

We show that under certain circumstances wide Aronszajn trees can be specialized iteratively without adding reals. We then use this fact to study forcing axioms compatible with CH and list some open problems.

15 Pages, submitted to the RIMS Set Theory and Infinity 2019 Kokyuroku, second version cleans up the exposition and fixes a gap in the proof of Lemma 3.6