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  "body": "\n## Summary\n\nA definable set in a [[structure|983GZBQYT4]] is a set of tuples of elements that is cut out by a first-order formula, possibly with parameters.\nDefinable sets are the main objects of study in modern model theory.\nTheir behaviour, such as in o-minimal or stable structures, describes how complicated a structure is.\n\n## Explanations\n\n### L1 human\n\nA definable set is a set that you can describe by a first-order formula in the language of the structure.\nIn the field of real numbers, the set of nonnegative numbers is definable by the formula \"$x$ is a square\", that is, $\\exists y \\, (y \\cdot y = x)$.\nThe unit circle is definable by $x \\cdot x + y \\cdot y = 1$.\nIn the ordered set $(\\R, \u003c)$ without parameters, no single number can be defined, because a shift $x \\mapsto x + c$ preserves the order.\n",
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