6月21日 - 6月25日, 7月26日 - 7月30日,

8月2日 - 8月6日

腾讯会议/Zoom会议（会议ID将根据注册情况以邮件形式发送）

宋诗畅 Shichang Song: Continuous First Order Logic

课时一: 9:00 - 10:15 (GMT+8)

课时二: 10:45 - 12:00 (GMT+8)

讨   论: 14:00 - 16:00 (GMT+8)

授课教师： 宋诗畅（Shichang Song），北京交通大学，数学系，副教授。博士毕业于伊利诺伊大学香槟分校。曾在中国科学院数学研究所从事博士后研究。学术研究领域是模型论及其在概率论，群论和组合数学的应用。在Fund. Math., MLQ Math. Log. Q., J. Korean Math. Soc.杂志发表论文多篇。

Rehana Patel: Model Theory

课时一: 14:30 - 15:45 (GMT+8)

课时二: 16:15 - 17:30 (GMT+8)

讨   论: (第二天) 9:30 - 11:30 (GMT+8)

授课教师： Rehana Patel is a mathematician working in the area of mathematical logic. Her research involves applications of model theory, a branch of mathematical logic, to the study of combinatorics and random structures.

Antonio Montalban: Scott complexity of countable structures

课时一: 8:00 - 9:15 (GMT+8)

课时二: 9:45 - 11:00 (GMT+8)

讨   论: 14:00 - 16:00 (GMT+8)

授课教师： Antonio Montalban is a mathematician at the University of California, Berkeley. He works in Mathematical Logic and, within Logic, he focuses on Computability Theory.  In general terms, his research studies the interplay between complexity and mathematics. Logicians have developed techniques to analyze and understand the complexity of many sorts of objects, including sets, structures, constructions, proofs, and so forth.  Computability Theory deals with the complexity measures used on countable objects, in contrast with, for instance, computer science or set theory, which mainly deal with the complexity of finite objects or uncountable objects, respectively.

Continuous First Order Logic

宋诗畅 Shichang Song

本课程讲述的连续一阶逻辑(continuous first order logic)，有时候也叫做度量结构的模型论(model theory for metric structures），连续模型论，或者就叫连续逻辑。它是由Ben Yaacov, Berenstein, Henson, Usvyatsov 在2008年前后发展起来的一种多值逻辑。连续一阶逻辑跟经典一阶逻辑最大的不同是，连续一阶逻辑的真值表是整个[0,1]区间。连续模型论作为模型论的一种推广，保持了很多模型论的特性，比如，连续模型论满足，紧致性定理，Lowenheim-Skolem 定理，可以定义型空间，讨论量词消解，范畴性和稳定性。本课程将从连续一阶逻辑的语法和语义出发，详细地讲述连续一阶逻辑的基础知识。最后，作为例子，介绍连续一阶逻辑在概率论中的应用。本课程只需要基础的一阶逻辑知识。

The lectures will be in Chinese.

参考文献:

■ I. Ben Yaacov, A. Berenstein, C. W. Henson and A. Usvyatsov, Model theory for metric structures, in: Model Theory with Applications to Algebra and Analysis, Volume 2, London Math. Society Lecture Note Series, 350, Cambridge University Press, 2008, 315-427.

■ I. Ben Yaacov and A. Usvyatsov, Continuous first order logic and local stability, Trans. Amer. Math. Soc. 362 (2010), 5213-5259.

课程计划：

Day 1: Metric structures, signatures, formulas, semantics

Day 2: Ultraproducts, Compactness Theorem, connectives

Day 3: Lowenheim-Skolem Theorem, types, definability

Day 4: Omitting types theorem, separably categoricity, quantifier elimination, stability

Day 5: Application to probability theory; probability algebras, random variable structures

Model Theory

Rehana Patel

TBA

Scott complexity of countable structures

Antonio Montalban

The lectures will be based on the following books with concentration on the Chapter II of the second book.

■ Computable Structure Theory: Within the Arithmetic.

■ Computable Structure Theory: Beyond the Arithmetic.

课程计划：

Day 1: Overview of the notions and the main results

Day 2: The Infinitary language

Day 3: (break)

Day 4: The back-and-forth relations

Day 5: Computable categoricity