Fragments of First-Order Logic germ the philosophical correspondences of these

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Fragments of First-Order Logic germ the philosophical correspondences of theseA sentence of first order logic is satisfiable if it is true in some structure, and finitely satisfiable if it is true in some finite structure. The question arises as to whether there exists an algorithm for determining whether a given formula of first order logic is satisfiable, or indeed finitely satisfiable. This question was answered negatively in 1936 by Church and Turing (for satisfiability) and in 1950 by Trakhtenbrot (for finite