Mathematical logic and foundations First-order logic Concept
Sentence
Summary
A sentence is a formula with no free variables. Every variable in it is bound by a quantifier, so it makes a complete claim. In a given structure a sentence is simply true or false, with no values to choose. Axioms of theories and theorems of mathematics are sentences.
Where this leads
19 pages build on this one.
- Compactness theorem
- Löb's theorem
- Diagonal lemma
- Fagin's theorem
- Model
- Craig interpolation theorem
- Skolem normal form
- Lindström's theorem
- Theory
- Elementary equivalence
- Ax–Grothendieck theorem
- Complete theory
- Gentzen's consistency proof
- Beth definability theorem
- Lefschetz principle
- Church's theorem on undecidability of first-order logic
- Gödel's completeness theorem
- Gödel's incompleteness theorems
- Tarski's undefinability theorem
Further reading
About this page
| Tag | DKFGQTRYZE |
|---|---|
| URI | m2://DKFGQTRYZE |
| Kind | concept |
| Writing | W0 stub |
| MSC | 03B10, 03C07 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Compactness theorem
- Löb's theorem
- Diagonal lemma
- Fagin's theorem
- Model
- Craig interpolation theorem
- Skolem normal form
- Lindström's theorem
- Theory
- Elementary equivalence
- Complete theory
- Lefschetz principle
- Church's theorem on undecidability of first-order logic
- Gödel's completeness theorem
- Gödel's incompleteness theorems
- Tarski's undefinability theorem