Logic and Foundations II
This is a continuation of my lecture on mathematical logic from the last semester. In this semester, we will move on to the theory of real closed fields, second order arithmetic, reverse mathematics and others.
Lecturer
Date
12th March ~ 11th June, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Thursday | 15:20 - 16:55 | A3-2-301 | ZOOM 07 | 559 700 6085 | BIMSA |
Prerequisite
"Logic and Foundations I". Those who did not take it should consult with me before enrolling this course.
Syllabus
In the last semester, we mainly studied basic model theory of first order logic, and subsystems of arithmetic and Gödel's incompleteness theorems. In this semester, we will discuss the following topics. (1) Models of first-order arithmetic (continued). (2) Real-closed ordered fields: completeness and decidability. (3) Theory of reals and reverse mathematics. (4) Second order arithmetic and non-standard methods. (5) Miscellaneous.
Reference
K. Tanaka, 数学基礎論序説 (in Japanese), Shokabo 2019.
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
Video Public
No
Notes Public
Yes
Language
English
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