Principles of Mathematical Logic

abbreviation algebra application argument places assertion axiom system bound variables cate combination of sentences conjunctive normal form connectives contains corresponding decision problem defined definition disjunction disjunctive normal form domain of individuals dyadic predicate elementary sentences Entscheidungsproblem equivalent Ex₁ example existential quantifiers false sentence free variables further given holds logical formulas Math mathematical means monadic predicates negation obtain predicate constants predicate F predicate variables predicates of second prefix prenex normal form primitive formula proof proved rational numbers real numbers relation replaced restricted predicate calculus Rule a3 Rule of Implication rules of inference satisfiability second level second-level predicate sentential calculus sentential combination sentential variables Skolem normal form syllogisms symbols system of axioms Theorem 34 theory tion transformed true formula true sentence truth value universal quantifier universally valid formulas variables occur X & Y X₁ Y₁