generalized continuum hypothesis

{{set theory}} The hypothesis that, for each ordinal <math>\alpha</math>, there is no cardinal number strictly between <math>\aleph_\alpha</math> and <math style="vertical-align:-0%;">2^{\aleph_\alpha}</math>, i.e. <math style="vertical-align:-20%;">2^{\aleph_\alpha}=\aleph_{\alpha+1}</math>.