{"id":"zfc-axioms","domain":"foundations-logic","type":"Concept","title":"ZFC Axioms","slug":"zfc-axioms","url":"/mathematics/foundations-logic/zfc-axioms/","summary":"Nine axioms of Zermelo-Fraenkel set theory with Choice — the standard foundation of modern mathematics. Developed 1908-1922 in response to Russell's Paradox.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Zermelo, E. (1908). Untersuchungen über die Grundlagen der Mengenlehre I. Mathematische Annalen, 65(2), 261-281."},{"tier":1,"citation":"Jech, T. (2003). Set Theory. 3rd millennium ed. Springer."},{"tier":2,"citation":"Enderton, H.B. (1977). Elements of Set Theory. Academic Press."},{"tier":3,"citation":"Halmos, P.R. (1960). Naive Set Theory. Van Nostrand."}],"relationships":[{"type":"foundational_for","target":"set","label":"Set"},{"type":"limited_by","target":"godels-incompleteness-theorems","label":"Gödel's Incompleteness Theorems"},{"type":"independence_example","target":"continuum-hypothesis","label":"Continuum Hypothesis"},{"type":"required_for","target":"proof","label":"Proof"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"2.3"}