MAT 407 Mathematical Logic
The course is dedicated to studying the reasoning processes and the relational systems common to all fields of mathematics and the relation between truth and proof in mathematics. The course begins by developing sentential logic and first-order logic, considers the soundness and completeness of these systems, and studies the properties of first-order theories and models, including the consequences of compactness. Finally, the Gödel Incompleteness Theorems are proved. Philosophical and practical implications of these results are discussed throughout the course.