Compactness theorem
Teorema de compacidad
- Date
- 1930 · confidence high
- Place
- Vienna, Austria
- Credited to
- Kurt Gödel, as a corollary of his completeness theorem for the countable case (1930); generalised to uncountable languages by Anatoly Maltsev (1936).
- Field
- Knowledge & symbols
What was discovered
States that a set of first-order formulas has a model if and only if every finite subset of it has one; a corollary of Gödel's completeness theorem and a key tool for constructing models.
What it led to
- Standard method for constructing non-standard models in model theory
- Central role, together with the downward Löwenheim-Skolem theorem, in Lindström's theorem on first-order logic
- Generalisation to uncountable languages by Anatoly Maltsev (1936)