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}}

.

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