Abstract
We prove within \({K(\mathbb{R})}\) that the axiom of determinacy is equivalent to the assertion that for each ordinal \({\lambda < \Theta}\) there exists a strong partition cardinal \({\kappa > \lambda}\). Here \({\Theta}\) is the supremum of the ordinals which are the surjective image of the set of reals \({\mathbb{R}}\).
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Cunningham, D.W. Strong partition cardinals and determinacy in \({K(\mathbb{R})}\) . Arch. Math. Logic 54, 173–192 (2015). https://doi.org/10.1007/s00153-014-0407-6
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DOI: https://doi.org/10.1007/s00153-014-0407-6