Determinacy and J\'onsson cardinals in $L(\mathbb{R})$

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

doi:10.1017/jsl.2014.49

Determinacy and J\'onsson cardinals in $L(\mathbb{R})$

Logic 2015-11-03 v3

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

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Abstract

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.

Keywords

determinacy J\'onsson cardinals Rowbottom cardinals $L(\mathbb{R})$ partition properties cofinality ZF+AD

Cite

@article{arxiv.1304.2323,
  title  = {Determinacy and J\'onsson cardinals in $L(\mathbb{R})$},
  author = {Steve Jackson and Richard Ketchersid and Farmer Schlutzenberg and W. Hugh Woodin},
  journal= {arXiv preprint arXiv:1304.2323},
  year   = {2015}
}

Comments

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

Determinacy and J\'onsson cardinals in $L(\mathbb{R})$

Abstract

Keywords

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