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Introduction to the Problems of the Foundations of Mathematics
Examples of Mathematical Domains
Selected Kinds of Relations and Functions
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antecedent applied arguments arithmetic of natural arithmetical hierarchy assumption axiom schema axiom system bounded called Comp computable functions computable relation computable set concept condition conjunction consequence consider consistent construction contains deduced denoted described disjunction elementary elements empty domain equiform Erec existential quantifier exists false finite number free variable function G function symbols Hence holds identity implication inductive definition infinite instance integers interpretation intuitive isomorphic less than relation logical theorem mathematical domain mathematical theories means metalogic names natural numbers negation normal form objects obtained occur one-to-one pairs predicate calculus predicate symbols prime number primitive recursive functions proved rational numbers real numbers recursively enumerable sets reference replaced rule of detachment schemata sentential calculus sentential connectives sentential formula set of numbers set of sentences set theory strongly representable strongly represents subsets superposition tautology term formula tion undecidable universal quantifier values well-formed formulae yields