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aconjunctive algebraic American Mathematical Society applied arithmetic arrows Association for Symbolic automorphism axiom of choice axiom system Boolean Borel c.e. sets calculus Cantor Church coding Coll comonad Comp Completeness Theorem Computer Science concept construction Corollary countable deduction theorem deductive completeness deductive system definable definition degrees denote Department of Mathematics Dept dissertation E-mail editors finite model theory finite structures first-order logic fixpoint formal functor Godel Hilbert implies induction infinite Inst isomorphic Journal of Symbolic Kechris Kleene Lambek language large cardinals linear logic Matematicas Math Mathematical Logic modal model theory natural numbers node notion objects obtained operation ordinal ordinal analysis P.O. Box paper Philos predicate problem proof theory propositional provable prove quantifiers recursion theory recursive functions recursively enumerable satisfies semantics sentences sequence set theory subset Symbolic Logic tableau Turing machine Univ University variables