Basics of Mathematical Logic
In this course, we explore the significant achievements and developments in the field of mathematical logic from the last century. Topics covered encompass first-order logic, recursion theory and computability, Gödel’s incompleteness theorems, model theory, and more.
讲师
日期
2023年09月18日 至 2024年01月09日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一 | 09:50 - 12:15 | A3-2a-302 | ZOOM 06 | 537 192 5549 | BIMSA |
课程大纲
1. First order logic: propositional logic, quantifiers, first-order languages and theories, normal forms and complexity.
2. Recursion theory and computability: primitive recursive functions, Turing machines and recursive functions, undecidability, complexity theory.
3. Gödel’s incompleteness theorems: the arithmetization of formal theories, incompleteness theorems.
4. Model theory: Gödel’s completeness theorem, compactness theorem, Lowenheim-Skolem-Tarski theorem, preservation theorems, complete theoreis.
2. Recursion theory and computability: primitive recursive functions, Turing machines and recursive functions, undecidability, complexity theory.
3. Gödel’s incompleteness theorems: the arithmetization of formal theories, incompleteness theorems.
4. Model theory: Gödel’s completeness theorem, compactness theorem, Lowenheim-Skolem-Tarski theorem, preservation theorems, complete theoreis.
听众
Undergraduate
, Graduate
视频公开
公开
笔记公开
公开
语言
中文
讲师介绍
蒋瀚如，现任BIMSA副研究员。他于2019年在中国科学技术大学获得计算机科学与技术博士学位。2019年至2020年间，在鹏城实验室量子计算研究中心担任助理研究员。主要研究方向包括程序设计语言理论、编译器的形式化验证以及量子计算中的程序语言问题。其研究成果多次发表于 PLDI、CAV、OOPSLA 等程序语言领域的顶尖国际会议及期刊，曾获 PLDI 2019 杰出论文奖。