Title: A Brief Introduction to Continuous Logic

Speaker: Shichang Song (Beijing Jiaotong University)

Time: 2025/04/29 (Tuesday) 15:10-18:00

Location: Room 215, Natural ​Sciences Teaching Building (理教), Peking University

Abstract: Continuous logic is a continuous version of first order logic, which was developed twenty years ago by Ben Yaacov, Berenstein, Henson, and Usvyatsov.The set of truth values in continuous logic is the interval [0,1] instead of the truth values {True,False} in classical logic. Also, the two quantifiers are sup and inf. Continuous logic still satisfies the compactness theorem, Lowenheim-Skolem theorems, existence of saturated and homogeneous models. During this talk, we will introduce syntax and semantics of continuous logic, ultraproduct constructions, types, definibility. At the end, we present some examples.