It is the negation of a weakened form,
, 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.
may also be called Luzin's hypothesis.
[2] The second continuum hypothesis is independent of Zermelo–Fraenkel set theory with the Axiom of Choice (ZFC): its truth is consistent with ZFC since it is true in Cohen's model of ZFC with the negation of the Continuum Hypothesis;[5][6]: 109–110 its falsity is also consistent since it is contradicted by the Continuum Hypothesis, which follows from V=L.
It is implied by Martin's Axiom together with the negation of the CH.