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Löwenheim–Skolem theorem
In mathematical logic, the classic Löwenheim–Skolem theorem states that for any countable first-order language L with signature langlemathbf{C}, mathbf{F}, mathbf{R}, sigmarangle and L-structure M, there exists a countably infinite elementary substructure N subseteq M. A natural and useful corollary of this theorem is that every consistent L-theory has a countable model.
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