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  "body": "\n## Summary\n\nA model of a [[theory|92SWXST1ZM]] is a [[structure|983GZBQYT4]] in which every sentence of the theory is true.\nModels give meaning to axioms: the models of the group axioms are exactly the groups.\nA theory with a model is consistent, and by [[Gödel's completeness theorem|WQ1ZE255SF]] every consistent first-order theory has a model.\n\n## Explanations\n\n### L1 human\n\nA theory is a list of rules, and a model is a concrete world in which all the rules hold.\nThe rules \"$\u003c$ is a strict linear order with no least and no greatest element\" have the integers with their usual order as a model.\nThe rational numbers with their usual order are another model of the same rules.\nThe set $\\set{1, 2, 3}$ with its usual order is not a model, because $1$ is a least element.\n",
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