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  "body": "\n## Summary\n\nA sentence is a [[formula|HYJ10AF6RT]] with no free variables.\nEvery variable in it is bound by a quantifier, so it makes a complete claim.\nIn a given [[structure|983GZBQYT4]] a sentence is simply true or false, with no values to choose.\nAxioms of theories and theorems of mathematics are sentences.\n\n## Explanations\n\n### L1 human\n\nThe formula $x \u003e 0$ is neither true nor false until you know $x$.\nThe sentence $\\forall x \\, (x \\cdot x \\ge 0)$ is a full claim: it is true in the real numbers.\nA sentence is a formula in which every variable is tied to a \"for all\" or a \"there exists\".\n",
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