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algebra algorithm American Mathematical Society arithmetic Association for Symbolic axioms Brouwer calculus choice sequences classical clauses cofinality Comp complete Computer Science concepts consistency construction continuum countable defined definition denote Department of Mathematics Dept derivation E-mail equivalent exists extension finite formula Germany Godel graph hierarchy inaccessible cardinal induction infinite inner model Inst intuitionistic iteration Journal of Symbolic Kechris Kleene labeled language large cardinals Lebesgue measurable Lemma linear linear logic lower bounds Math measurable cardinal modal logic model theory natural numbers node normal notion obtained ordinal P.O. Box paper Philos Philosophy predicate problem proof system proof theory properties propositional provable prove quantifiers real numbers recursion theory recursive functions regular cardinals relation rules semantics set of reals set theory singular cardinals Solovay structure subset Symbolic Logic Theorem tree Univ University variables Weyl Weyl's Woodin cardinals