generalized continuum hypothesis

English

Etymology

Generalization of the continuum hypothesis.

Noun

generalized continuum hypothesis

1. (set theory) The hypothesis that, for each ordinal $\alpha$, there is no cardinal number strictly between $\aleph _{\alpha }$ and $2^{\aleph _{\alpha }}$, i.e. $2^{\aleph _{\alpha }}=\aleph _{\alpha +1}$.