Mathematical logic and foundations Arithmetic and incompleteness Concept
Gödel numbering
Summary
A Gödel numbering assigns to each symbol, formula or proof of a formal language a natural number, its code, in an effective and injective way. It lets statements about formulas and proofs become statements about numbers. Gödel introduced it to prove his incompleteness theorems, where a theory of arithmetic talks about its own provability through codes.
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| Tag | MFJXPAF0R0 |
|---|---|
| URI | m2://MFJXPAF0R0 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 03F40 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Löb's theorem
- Diagonal lemma
- Provability logic
- Rice's theorem
- Kleene's recursion theorem
- Kleene's T predicate
- Gödel's incompleteness theorems
- Tarski's undefinability theorem
- Smn theorem
- Undecidability of the halting problem