Determinacy and Jónsson cardinals in $L(\mathbb{R})$

Steve Jackson, Richard Ketchersid, Farmer Schlutzenberg +1

Assume $\mathsf{ZF}+\mathsf{AD}+V=L(\mathbb{R})$ and let $\kappa <\Theta$ be an uncountable cardinal. We show that $\kappa$ is Jónsson, and that if $\mathrm{cof}(\kappa )=\omega$ then $\kappa$ is Rowbottom. We al…