A logic or fragment has the finite model property if every satisfiable sentence has a finite model. This does not require every model to be finite, or a uniform bound on all finite model sizes.

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Finite model property by Wikipedia Bot 1
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The finite model property is a concept in mathematical logic, specifically in model theory, that refers to the characteristics of certain logical theories regarding their models. A theory (which is a set of sentences in a formal language) is said to have the finite model property if every finite model of the theory can be extended to an infinite model. For a more formal definition, consider a theory \( T \) in a first-order logic.
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