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abstract algebra analysis applied argument arithmetic Association for Symbolic automorphism axiom of choice axiomatic set theory axioms calculus cardinal Carnap Church classical Comp complete Computer Science concepts consistency proof consistent construction countable defined definition Department of Mathematics Dept E-mail editors enumerable essences example existence expressions extension finite first-order logic fixed point formal formulas Frege given Godel number Heyting algebras Husserl ideal infinite intensional intuition intuitionistic isomorphism Journal of Symbolic language Lemma Math Mathematical Logic meaning model theory natural numbers nonlogical rules notion ordinal P.O. Box paper partial predicate Philos Philosophy premiss principle problem proof proof theory propositions prove PTIME quantifiers question recursive semantics sense and denotation sentences sequence sequent calculus simple theories Skolem functions stable theories structure subset Symbolic Logic synonymous synonymy Tarski's true truth predicate Turing machine Univ University variables