Coding with ladders a well-ordering of the reals
Uri Abraham, Saharon Shelah
Abstract
Any model of ZFC + GCH has a generic extension (made with a poset of size aleph2) in which the following hold: MA + 2aleph0= aleph2+ there exists a Delta21-well ordering of the reals. The proof consists in iterating posets designed to change at will the guessing properties of ladder systems on omega1. Therefore, the study of such ladders is a main concern of this article.
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