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.
Lecturer
Date
18th September, 2023 ~ 9th January, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday | 09:50 - 12:15 | A3-2a-302 | ZOOM 06 | 537 192 5549 | BIMSA |
Syllabus
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.
Audience
Undergraduate
, Graduate
Video Public
Yes
Notes Public
Yes
Language
Chinese
Lecturer Intro
Hanru Jiang obtained a Ph.D. in computer science and technology from the University of Science and Technology of China in 2019. From 2019 to 2020, he worked as an assistant research fellow at the Quantum Computing Research Center of Pengcheng Laboratory. In 2020, he joined BIMSA as an assistant professor. His main research directions are programming language theory, compiler verification, and programming language aspects in quantum computing. As the main contributor to the concurrent program separation compilation verification work CASCompCert, won the Distinguished Paper Award of PLDI 2019, a top conference in the field of programming languages.