{"id":"mathematical-logic","domain":"foundations-logic","type":"Concept","title":"Mathematical Logic","slug":"mathematical-logic","url":"/mathematics/foundations-logic/mathematical-logic/","summary":"Studies formal reasoning: propositional/predicate logic, proof theory, model theory, computability theory. Gave rise to Turing machines and the theoretical foundation of computer science.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Turing, A.M. (1936). On computable numbers. Proceedings of the London Mathematical Society, 42(1), 230-265."},{"tier":1,"citation":"Enderton, H.B. (2001). A Mathematical Introduction to Logic. 2nd ed."},{"tier":2,"citation":"Church, A. (1936). An unsolvable problem of elementary number theory. American Journal of Mathematics, 58(2), 345-363."},{"tier":3,"citation":"Hodges, A. (1983). Alan Turing: The Enigma."}],"relationships":[{"type":"related_to","target":"proof","label":"Proof"},{"type":"related_to","target":"zfc-axioms","label":"ZFC Axioms"},{"type":"foundational_to","target":"godels-incompleteness-theorems","label":"Gödel's Incompleteness Theorems"},{"type":"gave_rise_to","target":"big-o-notation","label":"Big-O Notation"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"2.4"}