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Syntax and Semantics
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A(exA arithmetic axiom of choice axiom schema B(eyB bound variables Chapter choice function Compactness Theorem conjunctive formula consistency proof Cut Elimination Cut Elimination Theorem defined definition denote derived rules e-calculus e-free formula e-symbol e-terms E2-axioms elementary formula exists a deduction ey(y finite subset following theorem formal language formal system formal theory free occurrence function symbol Hence Herbrand's Theorem Hilbert and Bernays identity symbol identity-free individual symbol induction hypothesis interpretation introduction rule Lemma logical closure logical subformula modus ponens normal refutation notation predicate calculus predicate symbol prenex formula proof of Theorem proper formula prove the consistency Q4-axiom quantifiers quasi-formula quasi-term rank result rules of inference satisfies Second e-Theorem sequent calculus set of formulae set theory structure rule substitution instance Suppose tautology rule term Theorem II1.2 theorem of 9 truth functionally truth value V-elimination vocabulary well-formed expression