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Coding with ladders a well ordering of the reals

Published online by Cambridge University Press:  12 March 2014

Uri Abraham
Department of Mathematics and Computer Science, Ben-Gurion University, Be'er-Sheva, Israel, E-mail:
Saharon Shelah
Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail:


Any model of ZFC + GCH has a generic extension (made with a poset of size ℵ2) in which the following hold: there exists a-well ordering of the reals, The proof consists in iterating posets designed to change at will the guessing properties of ladder systems on ω1. Therefore, the study of such ladders is a main concern of this article.

Research Article
Copyright © Association for Symbolic Logic 2002

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