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  "body": "\n## Summary\n\nAn o-minimal structure is a [[totally ordered|0FRXBVVR03]] structure in which every definable subset of the line is a finite union of points and open [[intervals|0Q1D85B8G6]].\nAn o-minimal theory is a theory all of whose models are o-minimal.\nThis condition on sets in one variable forces tame behaviour in all dimensions.\nDefinable sets admit cell decompositions and have a good dimension theory.\nThe ordered field of real numbers is the model case.\nO-minimality is the basis of \"tame geometry\", used in real algebraic geometry and in number theory.\n\n## Explanations\n\n### L1 human\n\nIn an o-minimal structure, a formula about one number can only describe a set made of finitely many points and intervals.\nYou can never describe an infinite discrete set such as the integers, or a set with infinitely many gaps.\nFor the real numbers with addition, multiplication and order, the inequality $x^2 - 2 \u003e 0$ describes $(-\\infty, -\\sqrt 2) \\cup (\\sqrt 2, \\infty)$, a union of two intervals.\nAdding the sine function would break this, because the zeros of sine form an infinite discrete set.\n",
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