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Full Idea
Paul Cohen showed that the Continuum Hypothesis is independent of the axioms of set theory.
Gist of Idea
The Continuum Hypothesis is independent of the axioms of set theory
Source
Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
Book Ref
Clegg,Brian: 'Infinity' [Robinson 2003], p.204