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The Origin of Modern Foundational Studies
Freges System and the Paradoxes
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abstract algebra axiom of choice axiom of extensionality axiom of infinity cardinal numbers category of sets category theory Chapter closed wff codomain consistent constant letters constructions contradiction defined Definition denumerable domain dummy constant equivalent example Exercise existence expression extensionality fact finite first-order system first-order theory formal system formula free variables Frege's function letters functor given global elements Godel number hypothesis induction interpretation intuitive isomorphic language mathematics means model for ST mono monomorphism morphisms natural deduction natural numbers nonempty normal model notion object obtain operation ordered pair ordinal paradox Peano postulates predicate calculus predicate letter principle proof proper axioms properties provable pullback quantifier real numbers recursive relation restriction result rules of inference satisfies Section sentence sequence set theory stratified subset system F Taut tautology term tion topos true type hierarchy type symbol type theory typical ambiguity unique vbtos