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Definition 2025

generalized_continuum_hypothesis

generalized continuum hypothesis

English

Noun

generalized continuum hypothesis ‎(uncountable)

(set theory) The hypothesis that, for each ordinal $\alpha$ , there is no cardinal number strictly between $\aleph _{\alpha }$ and $2^{\aleph _{\alpha }}$ , i.e. $2^{\aleph _{\alpha }}=\aleph _{\alpha +1}$ .