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  • A set of formulas T is a theory if it is closed under logical consequence. This means that, for every formula A , if T A , then A is in T

  • Let U be a set of formulas. Then, the set of all consequences of U

    T ( U ) = { A | U A }

    is called the theory of U . The formulas in U are called the axioms for the theory T(U) .

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