generalized continuum hypothesis

English

Etymology

A 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 ${\mathrm{\aleph }}_{\alpha }$ and $2^{{\mathrm{\aleph }}_{\alpha }}$, i.e. $2^{{\mathrm{\aleph }}_{\alpha }}={\mathrm{\aleph }}_{\alpha +1}$.