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Constants and variables
Propositions and propositional functions
24 other sections not shown
abbreviation applied functional calculus axiom of infinity binary functional variable brackets calculus of second cited in footnote consistent contains corresponding decision problem deduction theorem denotation derived rule disjunction domain of individuals elementary equivalence exercise expression finite formalized language formulation free occurrence free variables functional constants Hence Hilbert implication independence individual constant logistic system mathematical induction metatheorem method modus ponens natural numbers negation non-empty domain notation object language order with equality particular prefix premiss prenex normal form primitive connectives primitive symbols principal interpretation proof propositional form propositional functions propositional variables prove pure functional calculus quantifier-free ramified functional real numbers reduction result rule of substitution rules of inference satisfiable schema second order sense sentence singulary functional variables Skolem normal form syntactical system of domains system of postulates system of values tautology ternary theorem schemata truth-table truth-values undefined terms underlying logic w-ary functional variable well-formed formulas