Time: 2024/04/16 15:10-18:00

Location: Room 313, Teaching Building No.2 (第二教学楼), Peking University

Speaker 1: Xubing Deng

Title: Incompleteness via paradox

Abstract: In this talk, I will explore by mathematical means the relationship borne by the traditional paradoxes of set theory and semantics to formal incompleteness phenomena. A central tool is the application of the Arithmetized Completeness Theorem to systems of second-order arithmetic and set theory in which various "paradoxical notions" for first-order languages can be formalized. After introducing some preliminaries, I will provide two examples—Russell's paradox and the Liar—to show how paradoxes may be uniformly transformed into incompleteness theorems.

Speaker 2: Linzhen Gong

Title: 几何定理机器证明与Hilbert机械化定理

Abstract: Hilbert的《几何基础》在为欧式几何提供一个完整公理系统的同时，也蕴含了几何证明机械化的可能性。我们将在对“几何”概念精确化的基础上，从Hilbert公理系统（的一部分）出发，给出Desargues几何与Pascal几何的代数化方法。最后，我们将证明Hilbert关于Pascal几何中交点定理的机械化定理。