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Properties of the Propositional Calculus
26 other sections not shown
algorithm alphabet binary relation called cardinal Chapter computation congruence relation consistent subset construction countable Ded(A Deduction Theorem Definition denote diophantine element of P(V elementary group theory example Exercise exists finite subset First-Order Predicate Calculus first-order theory follows formalise free T-algebra given Godel number h(xu Hence homomorphism identical relation implies induction insoluble integers interpretation of P(V isomorphic Lemma Let 9 Let F logic mathematical model of 9 n-ary relation non-empty notation operation p e P(X pair Peano axioms polynomial Pred(F Predicate Calculus Prop(X proposition algebra Propositional Calculus prove quadruple quantifiers recursive function recursively enumerable relation symbol result satisfies p(x set theory Show Soundness Theorem standard real number standard system statement step string Suppose tape theorem of 9 theory 9 true truth function Turing machine ultrafilter ultrapower ultraproduct unique valuation var(p variables write