---
tag: DKFGQTRYZE
kind: concept
name: Sentence
msc: [03B10, 03C07]
sources:
  - url: https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)
same_as:
  wikidata: Q2509500
  wikipedia: Sentence (mathematical logic)
---

## Summary

A sentence is a [[formula|HYJ10AF6RT]] with no free variables.
Every variable in it is bound by a quantifier, so it makes a complete claim.
In a given [[structure|983GZBQYT4]] a sentence is simply true or false, with no values to choose.
Axioms of theories and theorems of mathematics are sentences.

## Explanations

### L1 human

The formula $x > 0$ is neither true nor false until you know $x$.
The sentence $\forall x \, (x \cdot x \ge 0)$ is a full claim: it is true in the real numbers.
A sentence is a formula in which every variable is tied to a "for all" or a "there exists".