Michael E. Townsend
Study of the first-order predicate calculus with identity and function symbols. Consistency, soundness, completeness, compactness. Skolem-Lowenheim theorem. Formalized theories. Prerequisite: PHIL 470.
Introduction to some of the fundamental limitative results of twentieth-century mathematical logic, including the non-computability results of Church, Tarski, and Turing, as well as Gödel’s First and Second Incompleteness Theorems. Prerequisites: PHIL 470 or equivalent (that is, a basic understanding of proof by induction, definition by recursion, and first-order logic). Some familiarity with axiomatic set theory would be helpful, but is not considered a requirement. TEXTS: No Textbook Required.
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