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.
讲师
日期
2024年03月12日 至 06月11日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周四 | 15:20 - 16:55 | A3-2-301 | ZOOM 07 | 559 700 6085 | BIMSA |
修课要求
"Logic and Foundations I". Those who did not take it should consult with me before enrolling this course.
课程大纲
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.
参考资料
K. Tanaka, 数学基礎論序説 (in Japanese), Shokabo 2019.
听众
Undergraduate
, Advanced Undergraduate
, Graduate
视频公开
不公开
笔记公开
公开
语言
英文
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。