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.
讲师
日期
2023年09月21日 至 2024年01月11日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周四 | 15:20 - 17:50 | Shuangqing-B725 | ZOOM 04 | 482 240 1589 | BIMSA |
课程大纲
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.
参考资料
K. Tanaka, 数学基礎論序説 (in Japanese), Shokabo 2019.
视频公开
不公开
笔记公开
公开
讲师介绍
田中一之教授博士毕业于美国加州大学伯克利分校，曾就职于东京工业大学和东北大学，并指导15位博士生和50名硕士生，2022年正式入职BIMSA。他是数理逻辑和计算理论领域的国际知名学者，在反推数学和二阶算术领域开创了新的研究方法，如WKLo的田中嵌入定理和守恒结果的田中公式，取得了一系列奠基性的成果，并将这一研究方向引入日本，将日本的数理逻辑研究推向了世界水平。田中一之教授还致力于模态mu演算，认知逻辑，随机博弈树等交叉领域的研究。