{"id":"continuum-hypothesis","domain":"foundations-logic","type":"Theorem","title":"Continuum Hypothesis","slug":"continuum-hypothesis","url":"/mathematics/foundations-logic/continuum-hypothesis/","posed":"1878, Georg Cantor","status":"independent","summary":"Is there a cardinality strictly between integers and reals? Proven independent of ZFC (Godel 1940 + Cohen 1963) - neither provable nor disprovable.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Cohen, P.J. (1963). The independence of the continuum hypothesis. PNAS, 50(6), 1143-1148."},{"tier":1,"citation":"Gödel, K. (1940). The Consistency of the Continuum Hypothesis. Princeton University Press."},{"tier":2,"citation":"Cohen, P.J. (1966). Set Theory and the Continuum Hypothesis. W.A. Benjamin."},{"tier":3,"citation":"Aczel, A.D. (2000). The Mystery of the Aleph."}],"relationships":[{"type":"built_on","target":"zfc-axioms","label":"ZFC Axioms"},{"type":"first_on","target":"hilberts-23-problems","label":"Hilbert's 23 Problems — Problem 1"},{"type":"related_to","target":"godels-incompleteness-theorems","label":"Gödel's Incompleteness Theorems"},{"type":"tracked_in","target":"proof-status","label":"Proof Status Board"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"2.3"}