## Foundations of Mathematics |

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abstract argument axiom of choice axiom of extensionality axiom of infinity cardinal numbers category of sets category theory Chapter closed wff codomain consistent constant letter constructions contradiction deduction defined Definition denumerable discussion domain element equivalent Exercise existence expressions finite first-order system first-order theory formal system foundation free variables Frege's function letters g x2 g x4 g xx given Godel number impredicative inaccessible cardinal induction infinite sets interpretation isomorphic iterating logical mapping mathematics means model for ZF morphisms natural numbers nonempty notion objects obtain occur ordered pairs ordinal paradox Peano postulates power set predicate calculus predicate letter principle proof properties provable quantifier reader will prove real numbers relation restriction result rules of inference Russell's Russell's paradox satisfy sentence sequence subset successor system F Taut tautology term operator true type hierarchy type symbol type theory wffs of F x2 g