= Axiom-only complete propositional calculus
Take precisely the <tautology>[propositional tautologies] as <axioms> and supply no <inference rules>. A one-line <formal proof>[proof] then establishes exactly the valid <propositional formulas>, so this calculus is sound and complete for <formal proof>[theoremhood]. Its <axiom>[axiom set] is decidable by finite <truth tables>. This construction does not by itself give strong completeness for consequence from arbitrary assumptions.
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