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Theory
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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
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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) .
