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

Abstract

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 also establish some other partition properties.

This version corresponds to the published version, including the title. Note that the formatting in the published version differs a little from this version. 17 pages