generalized continuum hypothesis

Generalization of the continuum hypothesis.

generalized continuum hypothesis

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