AD and Jónsson cardinals in L(R)

Steve Jackson, Richard Ketchersid, Farmer Schlutzenberg, W. Hugh Woodin

Published 2013-04-08, updated 2015-10-30Version 2

Assume $\mathsf{ZF}+\mathsf{AD}+V=L(\mathbb{R})$ and let $\kappa<\Theta$ be an uncountable cardinal. We show that $\kappa$ is J\'onsson, and that if $\mathrm{cof}(\kappa)=\omega$ then $\kappa$ is Rowbottom. We also establish some other partition properties.