LECTURE: Martin Zeman, Tu-Th 1:00 - 2:20 RH 510R
COURSE OBJECTIVES: The first half of the quarter will be devoted to basic axiomatic set theory. If time permits, we will discuss some basic cardinal arithmetic and stationary sets. The second half of the quarter will focus on Goedel's Completeness Theorem. We introduce first order languages, notions of satisfaction and formal proof, and prove three main theorems: Soundness theorem, Completeness theorem and Compactness theorem.
BOOK: I am not aware of a single book that would be suitable for
this course and which would cover both topics described above. Also, I will
not be using any book for the lecture. If you would like to have some book
that discusses the topics from the lecture, here are some suggestions.
Set theory:
Jech, Thomas: Set Theory
Kunen, Kenneth: Set Theory, and introducton to indepence proofs.
Schindler, Ralf: Set Theory. Exploring independence and truth.
First order Logic:
Enderton, Herbert: A mathematical introduction to logic.
GRADING: The final grade will be based on your homeworks and a take home final. There will be 5-8 homework assignments, depending on the progress in class.
HOMEWORK ASSIGNMENTS: HW1 HW2 HW3 HW4