Determinacy and Jónsson cardinals in $L(\mathbb{R})$
Assume $\mathsf{ZF}+\mathsf{AD}+V=L(\mathbb{R})$ and let $κ<Θ$ be an uncountable cardinal. We show that $κ$ is Jónsson, and that if $\mathrm{cof}(κ)=ω$ then $κ$ is Rowbottom. We also establish some other partition properties.
math.LO↗