Logic and Foundations I
This is an advanced undergraduate and graduate-level course in mathematical logic and foundations of mathematics. It is almost complementary to my last courses ”Logic and Computation I and II.” So, completion of them is recommended but not required. If not completed, please self-study with the slides uploaded on the lecture page at BIMSA.
Lecturer
Date
21st September, 2023 ~ 11th January, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Thursday | 15:20 - 17:50 | Shuangqing-B725 | ZOOM 04 | 482 240 1589 | BIMSA |
Syllabus
Topics to be presented in the first semester include: theory of equations, Birkhoff’s completeness theorem, Boolean algebras, Gentzen-Tait proof sysytem, Goedel’s completeness theorem, basic model theory, ultra-products, non-standard analysis, subsystems of first order arithmetic, Presburger arithmetic, non-standard models of arithmetic, saturated models, etc. In the second semester, we will move on to theory of real closed fields, second order arithmetic and reverse mathematics.
Reference
K. Tanaka, 数学基礎論序説 (in Japanese), Shokabo 2019.
Video Public
No
Notes Public
Yes
Lecturer Intro
Kazuyuki Tanaka received his Ph.D. from U.C. Berkeley. Before joining BIMSA in 2022, he taught at Tokyo Inst. Tech and Tohoku University, and supervised fifteen Ph.D. students. He is most known for his works on second-order arithmetic and reverse mathematics, e.g., Tanaka's embedding theorem for WKLo and the Tanaka formulas for conservation results. For more details: https://sendailogic.com/tanaka.html