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Full Idea
Gödel proved that the Continuum Hypothesis was not inconsistent with the axioms of set theory.
Gist of Idea
The Continuum Hypothesis is not inconsistent with the axioms of set theory
Source
report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15
Book Ref
Clegg,Brian: 'Infinity' [Robinson 2003], p.203