Second continuum hypothesis

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 (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.