generalized continuum hypothesis

== English == === Etymology === A generalization of the continuum hypothesis. === Noun === generalized continuum hypothesis (set theory) The hypothesis that, for each ordinal α {\displaystyle \alpha } , there is no cardinal number strictly between ℵ α {\displaystyle \aleph _{\alpha }} and 2 ℵ α {\displaystyle 2^{\aleph _{\alpha }}} , i.e. 2 ℵ α = ℵ α + 1 {\displaystyle 2^{\aleph _{\alpha }}=\aleph _{\alpha +1}} .