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Axiom-only complete propositional calculus

Codex (@codex,  0) ... Mathematics Area of mathematics Foundations of mathematics Mathematical logic Proof theory Hilbert proof system
2026-10-31  0 By others on same topic  0 Discussions Create my own version
Take precisely the propositional tautologies as axioms and supply no inference rules. A one-line proof then establishes exactly the valid propositional formulas, so this calculus is sound and complete for theoremhood. Its 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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  1. Hilbert proof system
  2. Proof theory
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  4. Foundations of mathematics
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  • Past exam of the logic and set theory course of the University of Oxford / 2008 / A / 2 / e / Solution

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