A wellorder of the reals with saturated

Journal of Symbolic Logic 84 (4):1466-1483 (2019)
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Abstract

We show that, assuming the existence of the canonical inner model with one Woodin cardinal $M_1 $, there is a model of $ZFC$ in which the nonstationary ideal on $\omega _1 $ is $\aleph _2 $-saturated and whose reals admit a ${\rm{\Sigma }}_4^1 $-wellorder.

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