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Coding with ladders a well ordering of the reals
Journal of Symbolic Logic 67 (2):579-597 (2002)
Abstract
Any model of ZFC + GCH has a generic extension (made with a poset of size ℵ 2 ) in which the following hold: MA + 2 ℵ 0 = ℵ 2 +there exists a Δ 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 ω 1 . Therefore, the study of such ladders is a main concern of this articleOther Versions
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Citations of this work
Large cardinals and locally defined well-orders of the universe.David Asperó & Sy-David Friedman - 2009 - Annals of Pure and Applied Logic 157 (1):1-15.
Forcing lightface definable well-orders without the GCH.David Asperó, Peter Holy & Philipp Lücke - 2015 - Annals of Pure and Applied Logic 166 (5):553-582.
References found in this work
A Δ22 well-order of the reals and incompactness of L.Uri Abraham & Saharon Shelah - 1993 - Annals of Pure and Applied Logic 59 (1):1-32.
Martin's axiom and $\Delta^2_1$ well-ordering of the reals.Uri Abraham & Saharon Shelah - 1996 - Archive for Mathematical Logic 35 (5):287-298.
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