Let Σ be an effectively countable set of formulas. Suppose that for each formula τ, either Σ⊨τ or Σ⊨¬τ. Prove that the set of tautological consequences of Σ is decidable.

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Mathematical logic

Formula set properties.

Let Σ be an effectively countable set of formulas. Suppose that for each formula τ, either Σ⊨τ or Σ⊨¬τ. Prove that the set of tautological consequences of Σ is decidable.

Please be as clear as possible. Use definitions if necessary. Show and explain all the steps of the proof. Thank you.

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