Mathematical Logic and Hilbert's & Symbol |
Contents
Introduction | 1 |
Syntax and Semantics | 9 |
Formal Systems | 37 |
Copyright | |
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Common terms and phrases
&*-calculus A₁ arithmetic atom axiom of choice axiom schema B(ɛyB B₁ bound variables choice function Consequently consistency proof Cut Elimination Theorem cut rule defined definition denote derived rules e-calculus e-free formulae e-symbol E2-axioms elementary formula existential formula ɛ-free ɛ-term ɛxA ɛy(y ɛyB F-Ref(A F-refutation finitary finite following theorem formal system formulae of L(V free occurrence function symbol Hence Herbrand's Theorem Hilbert and Bernays identity symbol identity-free immediate logical subformula ind(A individual symbol induction hypothesis introduction rule Lemma major formula mathematical modus ponens normal refutation obtained predicate calculus predicate symbol prenex formula proof of Theorem proper formula Q4-axiom quantifier-free proof quasi-formula quasi-term rank Ref(A replacing each occurrence result rules of inference Second &-Theorem sequent calculus set of formulae set theory Skolem functions structure rule substitution instance t₁ tautology rule term truth value V-elimination vocabulary y-rule