Any model of ZFC + GCH has a generic extension (made with a poset of size aleph_2) in which the following hold: #R##N#MA + 2^{aleph_0}= aleph_2+ there exists a Delta^2_1-well ordering of the reals. #R##N#The proof consists in iterating posets designed to change at will the guessing properties of ladder systems on omega_1. Therefore, the study of such ladders is a main concern of this article.
['Uri Abraham', 'Saharon Shelah']
Coding with ladders a well-ordering of the reals