---
tag: VR1AGNPR34
kind: statement
role: proposition
name: Second continuum hypothesis
aliases: [lusin-hypothesis, lusins-hypothesis, lusins-second-continuum-hypothesis, luzin-hypothesis, luzins-hypothesis, luzins-second-continuum-hypothesis]
sources:
  - wikipedia: en:75602409@r1354289583
    locator: Second continuum hypothesis
    note: adopted
    mention: wikipedia://en/75602409
    sections: [Statement]
same_as:
  wikidata: Q124096694
  wikipedia: Second continuum hypothesis
inventory: [QCZCS49XN9]
---

## Statement

The **second continuum hypothesis**, also called **Luzin's hypothesis** or **Luzin's second continuum hypothesis**, is the hypothesis that $2^{\aleph_0}=2^{\aleph_1}$. It is the negation of a weakened form, $2^{\aleph_0}<2^{\aleph_1}$, of the [[continuum hypothesis|0MN2MER9WN]] (CH). It was discussed by Nikolai Luzin in 1935, although he did not claim to be the first to postulate it.p. 157, 171p. 130-131 The statement $2^{\aleph_0}<2^{\aleph_1}$ may also be called Luzin's hypothesis.