---
tag: 4CHX0XF5GB
kind: statement
role: proposition
name: Weak continuum hypothesis
sources:
  - wikipedia: en:75603109@r1329908310
    locator: Weak continuum hypothesis
    note: adopted
    mention: wikipedia://en/75603109
    sections: [Statement]
same_as:
  wikidata: Q124096710
  wikipedia: Weak continuum hypothesis
inventory: [6E0E2F032Y]
---

## Statement

The term **weak continuum hypothesis** can be used to refer to the hypothesis that $2^{\aleph_0}<2^{\aleph_1}$, which is the negation of the second continuum hypothesis.p. 80p. 3616 It is equivalent to a weak form of ◊ on $\aleph_1$.p. 2 F. Burton Jones proved that if it is true, then every [[separable|0GKJ78948V]] [[normal|0AJ646N339]] Moore space is metrizable.