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arXiv · 1803.08201

$L(\mathbb{R})$ with Determinacy Satisfies the Suslin Hypothesis

William Chan·Stephen Jackson
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Abstract

The Suslin hypothesis states that there are no nonseparable complete dense linear orderings without endpoints which have the countable chain condition. $\mathsf{ZF + AD^+ + V = L(\mathscr{P}(\mathbb{R}))}$ proves the Suslin hypothesis. In particular, if $L(\mathbb{R}) \models \mathsf{AD}$, then $L(\mathbb{R})$ satisfies the Suslin hypothesis, which answers a question of Foreman.

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William Chan, Stephen Jackson. 2018-03-22. $L(\mathbb{R})$ with Determinacy Satisfies the Suslin Hypothesis. https://arxiv.org/abs/1803.08201

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