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1-Steiner cover arithmetic assume atoms axiom of choice axioms of infinity binary relation Boolean algebra characterizable cofinal complete complete Boolean algebra condition consistent construction continuum hypothesis contradiction COROLLARY countable defined definition denote element elementary elementary submodel elementary substructure equivalent exists extended extensional fact finite sets formula free variables function f functor given Godel Hence hierarchy implies inaccessible cardinal induction infinite integers intuitionistic isomorphic LEMMA limit ordinal logic main numbers mapping measurable cardinal model of ZF monotony laws morphism non-zero cardinal numbers normal notion obtain operations power set predicate principle Proof provable prove quantifiers recursive regular cardinal relation replacing restricted result satisfies second-order sentence sequence set theory Solovay statement submodel subset Suppose THEOREM transfinite transitive model uncountable universe well-ordering