Foundations of mathematical logic
Class Hours: Thu 1:15–3:40 PM
Class Room: Chengjun complex 4, 611
Office Hours: Wed 3-5 PM (or by appointment)
Mathematical logic is the study of formal logic as a branch of mathematics. This course serves as a graduate-level introduction to mathematical logic. As such it covers its fundamental concepts with emphasis on elementary set theory, formal propositional languages and grammars, truth tables, natural deduction, proof normalization, formal first-order languages and grammars, first-order semantics, soundness and completeness, compactness and Löwenheim-Skolem, quantifier elimination, prenex normal forms, Herbrand's theorem, the theory of recursive functions, Peano arithmetic, and Gödel’s incompleteness results.
Basic knowledge of mathematics such as elementary set theory is desirable, but not necessary. If you think such concepts can be challenging for you, it would be wise to devote some extra time to the course and practice your skills with extra exercises from the textbook. If you are still having trouble keeping up with the classes, please talk to me. Learning logic can be a really fun experience and I want you to enjoy taking this course.
This course is roughly based on the fourth edition of the textbook:
Van Dalen, Dirk. Logic and Structure. ISBN: N 978-3-540-20879-2.
For more information on the course assessment and schedule please check the syllabus available below.
Here I list some links to materials from the course:
Please let me know if you find any broken links.