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  "body": "\n## Definition\n\nLet $L$ be a signature, let $\\mathcal{M}$ be an $L$-[[structure|983GZBQYT4]] with domain $M$, and let $A \\subseteq M$.\nA set $X \\subseteq M^n$ is definable with parameters from $A$ when there are an $L$-[[formula|HYJ10AF6RT]] $\\varphi(x_1, \\dots, x_n, y_1, \\dots, y_m)$ and $b_1, \\dots, b_m \\in A$ such that\n$$X = \\set{(a_1, \\dots, a_n) \\in M^n : \\mathcal{M} \\models \\varphi(a_1, \\dots, a_n, b_1, \\dots, b_m)}.$$\nThe set $X$ is definable when it is definable with parameters from $M$.\nIt is definable without parameters, or $\\emptyset$-definable, when it is definable with parameters from $\\emptyset$.\n\n## Remarks\n\nExample: in the field $(\\R, +, \\cdot, 0, 1)$, the set $[0, \\infty)$ is definable without parameters by $\\varphi(x) = \\exists y \\, (y \\cdot y = x)$.\nIndeed a real number is a square of a real number exactly when it is nonnegative.\n\nNon-example: in $(\\R, \u003c)$, the set $\\set{0}$ is not definable without parameters.\nThe map $\\sigma(x) = x + 1$ is an automorphism of $(\\R, \u003c)$, and an automorphism maps each $\\emptyset$-definable set onto itself; but $\\sigma(\\set{0}) = \\set{1}$.\nWith the parameter $0$, the formula $x = y_1$ defines $\\set{0}$.\n\nThe definable subsets of $M^n$ are closed under finite unions, finite intersections and complements, and projections of definable sets are definable.\n\n## Explanations\n\n### L1 human\n\nThe definable sets are the sets that the language of the structure can describe.\nAllowing parameters means that the description may name finitely many fixed elements.\n",
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      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
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      {
        "what": "a source with a locator",
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