generalized continuum hypothesis
Noun
Meaning
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}}
.