Full Idea
As we have known since Paul Cohen's theorem, the Continuum Hypothesis is intrinsically undecidable. Many believe Cohen's discovery has driven the set-theoretic project into ruin, or 'pluralized' what was once presented as a unified construct.
Gist of Idea
The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory
Source
Alain Badiou (Briefings on Existence [1998], 6)
Book Reference
Badiou,Alain: 'Briefings on Existence', ed/tr. Madarsz,Norman [SUNY 2006], p.99
A Reaction
Badiou thinks the theorem completes set theory, by (roughly) finalising its map.