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  "body": "\n## Summary\n\nTwo [[structures|983GZBQYT4]] for the same signature are elementarily equivalent when they satisfy the same first-order sentences.\nIsomorphic structures are elementarily equivalent, but the converse fails.\nElementary equivalence is the notion of \"sameness\" that first-order logic can see.\n\n## Explanations\n\n### L1 human\n\nImagine that you may only ask yes-or-no questions written as first-order sentences.\nTwo structures are elementarily equivalent when every such question gets the same answer in both.\nThe ordered sets $(\\Q, \u003c)$ and $(\\R, \u003c)$ are elementarily equivalent, although one is countable and the other is not.\nThe ordered sets $(\\Z, \u003c)$ and $(\\Q, \u003c)$ are not, because \"between any two elements there is a third\" is true in $\\Q$ and false in $\\Z$.\n",
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