Generalized continuum hypothesis

English

Etymology

Generalization of the continuum hypothesis.

Noun

1. Template:Lb The hypothesis that, for each ordinal $\alpha$, there is no cardinal number strictly between ${\mathrm{\aleph }}_{\alpha }$ and $2^{{\mathrm{\aleph }}_{\alpha }}$, i.e. $2^{{\mathrm{\aleph }}_{\alpha }}={\mathrm{\aleph }}_{\alpha +1}$. Template:C