Mathematical logic and foundations First-order logic Concept
Well-formed formula
Summary
A well-formed formula, or simply formula, is a string of symbols built by the grammar of a formal language. In first-order logic, formulas are built from atomic formulas with connectives and quantifiers. Formulas are the objects that proofs manipulate and that structures make true or false. Only well-formed strings have a meaning, so the definition is the first step of every formal logic.
Where this leads
22 pages build on this one.
- Prenex normal form
- Elementary substructure
- Diagonal lemma
- Transfer principle
- Tarski–Vaught test
- Gödel numbering
- Elementary embedding
- Łoś's theorem
- Arithmetical hierarchy
- Infinitary logic
- Nonstandard analysis
- NIP theory
- Satisfiability
- Logical consequence
- Morley rank
- Sentence
- Quantifier elimination
- Beth definability theorem
- Type
- Second-order arithmetic
- Tarski's undefinability theorem
- Definable set
Further reading
About this page
| Tag | HYJ10AF6RT |
|---|---|
| URI | m2://HYJ10AF6RT |
| Kind | concept |
| Writing | W0 stub |
| MSC | 03B10, 03B05 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Prenex normal form
- Elementary substructure
- Diagonal lemma
- Tarski–Vaught test
- Gödel numbering
- Elementary embedding
- Łoś's theorem
- Arithmetical hierarchy
- Infinitary logic
- NIP theory
- Satisfiability
- Logical consequence
- Morley rank
- Sentence
- Quantifier elimination
- Beth definability theorem
- Type
- Second-order arithmetic
- Tarski's undefinability theorem
- Definable set