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  1. A theory is as a pair $(\Sigma;\mathcal{A})$ where $\Sigma$ is a signature
  2. which defines a set of constant, function, and predicate symbols.
  3. The set of axioms $\mathcal{A}$ is a set of closed predicate logic formulas in which only
  4. constant, function, and predicate symbols of $\Sigma$ appear.