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  "body": "\n## Summary\n\nA signature lists the non-logical symbols of a first-order language: function symbols, relation symbols and constant symbols, each with its number of arguments.\nIt fixes what one can talk about, before any axioms are chosen.\nTerms, formulas and [[structures|983GZBQYT4]] are always taken over a given signature.\nAnother name is vocabulary, and in Mathlib it is called a first-order language.\n\n## Explanations\n\n### L1 human\n\nBefore writing axioms for groups, one has to say which symbols are allowed.\nFor groups, one may take a binary symbol $\\cdot$, a unary symbol ${}^{-1}$ and a constant $e$.\nThis list of symbols with their numbers of arguments is the signature.\nThe axioms, such as associativity, come later and are not part of the signature.\n",
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