Determinacy and J\'onsson cardinals in L(mathbb{R})
classification
🧮 math.LO
keywords
kappamathbbmathsfonssonassumecardinalcardinalsdeterminacy
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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.
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