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

William Chan; Stephen Jackson

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

Logic 2018-03-23 v1

Authors: William Chan , Stephen Jackson

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.

Keywords

set theory additive number theory

Cite

@article{arxiv.1803.08201,
  title  = {$L(\mathbb{R})$ with Determinacy Satisfies the Suslin Hypothesis},
  author = {William Chan and Stephen Jackson},
  journal= {arXiv preprint arXiv:1803.08201},
  year   = {2018}
}

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

Abstract

Keywords

Cite

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