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 is an Associate Researcher at BIMSA. He received his Ph.D. in Computer Science and Technology from the University of Science and Technology of China in 2019. From 2019 to 2020, he was an Assistant Researcher at the Quantum Computing Research Center, Peng Cheng Laboratory. His research interests lie in programming language theory, formal verification of compilers, and programming language issues in quantum computing. His work has been published in premier venues such as PLDI, CAV, and OOPSLA. He was a recipient of the PLDI 2019 Distinguished Paper Award.