Martin's axiom and $\Delta^2_1$ well-ordering of the reals

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Archive for Mathematical Logic 35 (5-6):287-298 (1996)
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Abstract

Assuming an inaccessible cardinal $\kappa$ , there is a generic extension in which $MA + 2^{\aleph_0} = \kappa$ holds and the reals have a $\Delta^2_1$ well-ordering

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10.1007/s001530050046

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original Abraham, Uri; Shelah, Saharon (1996) "Martin's axiom and well-ordering of the reals". Archive for Mathematical Logic 35(5):287-298

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Coding with ladders a well ordering of the reals.Uri Abraham & Saharon Shelah - 2002 - Journal of Symbolic Logic 67 (2):579-597.

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