Coding with ladders a well ordering of the reals

by Abraham and Shelah. [AbSh:485]
J Symbolic Logic, 2002
Any model of ZFC + GCH has a generic extension (made with a poset of size aleph_2) in which the following hold: MA + 2^{aleph_0}= aleph_2+ there exists a Delta^2_1 - well ordering of the reals. 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.


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