{
  "id": "computability-theory",
  "domain": "foundations-logic",
  "type": "Concept",
  "title": "Computability Theory",
  "slug": "computability-theory",
  "url": "/mathematics/foundations-logic/computability-theory/",
  "summary": "Studies which problems are solvable by any algorithm. Turing 1936 halting problem undecidable; Rice's theorem; arithmetical hierarchy; Turing degrees; priority method (Friedberg-Muchnik 1957).",
  "added_to_codex": "2026-07-09",
  "last_verified": "2026-07-09",
  "sources": [
    {
      "tier": 1,
      "citation": "Turing, A.M. (1936). On computable numbers. Proc. London Math. Soc., 42(1), 230-265."
    },
    {
      "tier": 1,
      "citation": "Soare, R.I. (2016). Turing Computability: Theory and Applications. Springer."
    },
    {
      "tier": 2,
      "citation": "Sipser, M. (2012). Introduction to the Theory of Computation. 3rd ed."
    },
    {
      "tier": 3,
      "citation": "Hodges, A. (1983). Alan Turing: The Enigma."
    }
  ],
  "entry_status": "live",
  "reading_levels_available": [
    "curious",
    "exploring",
    "deep_dive"
  ],
  "completeness": 1.0,
  "codex_version": "2.5"
}