$\omega$ $\aleph$ $\infty$
Mathematical Logic at Fudan

### 2022 Fudan Logic Summer School

Zoom Meeting invitation for the second week has been send. Please let us know if you have enrolled for the second week yet not received the email.

Date: Jul 4 - 8, Jul 18 - 22

Location: Zoom Meeting (Meeting ID To be send via email according to the registration)

In case the Zoom Meeting room if full, you can watch the live here.

Schedule

#### The first week (Jul 4 - Jul 8): 叶谨赫 Jinhe Ye (Vincent): 赋值域 Valued Fields (in Chinese).

• Lecture1: 15:00 - 16:15 (GMT+8)
• Lecture2: 16:45 - 18:00 (GMT+8)
• Section: (Next day) 10:00 - 12:00 (GMT+8)

#### The second week (Jul 18 - Jul 22):Gabriel Goldberg: Large cardinals beyond the Axiom of Choice.

• Lecture 1: 12:00 - 13:15 (GMT+8)
• Lecture 2: 13:45 - 15:00 (GMT+8)
• Section: 9:00 - 10:00 (GMT+8)
The section of the second week will be lead by Jason Chen (陈泽晟) and start from Jul 18, which is before the first lecture.

Model Theory

### 赋值域 Valued Fields

The lectures will be in Chinese.

#### Program:

• Day 1: Normed fields, valued fields and Henselianity. Video
• Day 2: Extensions of valuations. Video
• Day 3: Algebraically closed valued fields. Video
• Day 4: Henselian fields and Kaplansky theory. Video
• Day 5: Ax-Kochen-Ershov and Artin conjecture. Video

Set Theory

### Large cardinals beyond the Axiom of Choice

#### Program:

• Day 1: Introduction to choiceless large cardinals. Video Slides Exercise
Section: Prerequisite (by Jason Chen). Video Notes
• Day 2: Measurable cardinals and constructibility, ordinal definablility and the HOD conjecture. Video Slides Notes Exercise
Section: Exercise 01 (by Jason Chen). Video
• Day 3: Periodicity in the cumulative hierarchy. Video Notes Exercise
Section: Exercise 02 (by Jason Chen). Video
• Day 4: Simulating the Axiom of Choice, the structure of the club filter. Video Notes Exercise
Section: Exercise 03 (by Jason Chen). Video
• Day 5: Measures on ordinals, the $\theta_\alpha$ sequence. Video
Section: Exercise 04 (by Jason Chen). Video

#### Lecturer:

Gabriel Goldberg is an assistant professor at the department of mathematics, at UC Berkeley. He is working in set theory, interested in large cardinals, inner models, and infinite combinatorics. He has published some important papers in large cardinal and inner models in JML and JSL in recent years. He is also writing the book The Ultrapower Axiom.

Organizers

Contact: logic@fudan.edu.cn

2022复旦大学数理逻辑暑期学校由复旦大学教务处主办，复旦大学哲学学院逻辑学教研室承办