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  "body": "\n## Summary\n\nModel theory is the branch of mathematical logic that studies formal [[theories|92SWXST1ZM]] together with their [[models|MVCH6N9SNW]].\nIt asks which classes of [[structures|983GZBQYT4]] a set of axioms describes, and which subsets of a structure a formal language can define.\nIts tools, such as the [[compactness theorem|1NR3HAWG9D]], have applications in algebra, number theory and geometry.\n\n## Explanations\n\n### L1 human\n\nModel theory looks at mathematics from two sides at once: the sentences you write and the objects that make them true.\nFor example, the field axioms are sentences, and the fields $\\Q$, $\\R$ and $\\C$ are objects that satisfy them.\nA typical question is: if two structures satisfy the same sentences, how alike must they be?\nAnother is: which sets of points can a formula describe inside a given structure?\n",
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