## Fudan Logic Student Seminar 2023

### December 19

Speaker: 邬舒雯 Shuwen Wu

Time: 13:15 - 14:30. Location: HGW2403.

#### The Analysis of Leitgeb's Truth Standards

In this talk, we build upon Leitgeb's article 'What Theories of Truth Should Be Like,' engaging in a comprehensive discussion and analysis of the eight standards he proposes for truth theories. While exploring these standards, our focus will be on their theoretical foundations, logical structures, and practical feasibility. The aim is to gain a deeper understanding of the guiding role these standards play in truth theories and to distill key elements for constructing an exemplary truth theory. Simultaneously, we reexamine classical literature on truth theories, seeking a more holistic perspective to comprehend the strengths and weaknesses of different theories.

Speaker: 周佳楠 Jianan Zhou

Time: 14:30 - 15:45. Location: HGW2403.

#### From Stone Duality to Classifying Topos

Throughout mathematical logic, there's a reoccuring theme of duality between geometry and logic. This is called Stone duality, in honor of Marshall Stone who discovered the first instance of such duality between Boolean algebras and Stone spaces. Stone duality extends all the way to the powerful theory of topos, as first noted by Grothendieck, the founder of topos. From this perspective, topos theory becomes "just another kind of logic" (namely, geometric logic) which one can understand without delving into heavy categorical machinery, and I would argue that this is the conceptually correct approach. This talk is intended to introduce the basic idea of topos to a wider range of logicians. Audiences are expected to have some familiarity with basic category theory and mathematical logic. Slides

### November 7

Speaker: 鞠大恒 Daheng Ju

Time: 13:15 - 14:30. Location: HGW2403.

#### The Graph Conception of Set and Non-Well-Founded Set Theories

The graph conception of set, proposed by Luca Incurvati in 2014, aims to provide philosophical justification for non-well-founded set theories. In addition, Incurvati also attempts to argue that the graph conception of set justifies a specific non-well-founded set theory - AFA set theory. In this talk, I will critically examine Incurvati's work and show that even if the graph conception of set is accepted, it remains unresolved which non-well-founded set theory is justified.

Speaker: 周佳楠 Jianan Zhou

Time: 14:30 - 15:00. Location: HGW2403.

#### Foundation Should be Proof-Relevant

Classically, mathematics and a part of analytic philosophy are considered to be based on first-order logic and ZFC set theory. I believe that many philosophical problems are directly due to the highly proof-irrelevant nature of first-order logic. In this short presentation, I will explain the concept of proof relevance and try to argue why it's should be a feature of our foundational theory.

Due to time constraints, the presentation will skip technical details and will focus exclusively on ideas and motivations. No knowledge background is required except for basic mathematical logic and an open mind.

### September 26

Speaker: 张芷青 Zhiqing Zhang

Time: 13:30 - 15:00. Location: HGW2401.

#### Universe in type theory and its relation to large cardinal

This talk is an introduction of 'universe' in type theory and its relation to large cardinal in set theory. In this talk, some basic concepts of type theory and type universe will be introduced. It serves as a part of the background of my master's thesis. This talk is based on several papers: 'The type theoretic interpretation of constructive set theory' by Peter Aczel; 'On universe in type theory' by Erik Palmgren; 'Inaccessibility in constructive set theory and type theory' by Michael Rathjen.

### September 12

Speaker: 唐哲 Zhe Tang

Time: 13:15 - 15:10. Location: HGW2403.

#### History of Shelah conjecture

This talk is actually an introduction of reading group of model theory for this semester. We are going to come across three important roadmarks towards the classification of NIP fields. We are trying to explain the strength among them and give people a general idea of this topic. Hopefully, people can understand the idea behind these progress.

### May 19

Speaker: 张芷青 Zhiqing Zhang

Time: 11:45 - 13:15. Location: HGW2403.

#### Characterization of measurable cardinal in category theory

The answers to certain questions in category theory turn out to depend on set theory. Based on previous works, we know the existence of measurable cardinal is equivalent to the existence of non-identity exact endofunctor on SET. This is give by the relation between weakly representable functor and reduce power, and we will see, reduce non-principle ultrafilter is a non-identity exact endofunctor. Further more, with some simple check, we find that a functor with those properties would give us a non-principle ultrafilter, which is similar to regular ultrafilter given by an elementary embedding with its critical point. This talk is based on *Exact functor and measurable cardinal* by Andreas Blass.

### May 12

Speaker: 魏晋 Jin Wei

Time: 11:45 - 13:15. Location: HGW2403.

#### Continuous Logic Saga and a Search for Its Gentzen-style Proof System

Continuous model theory was revived and draws huge attention over the past decade. The idea is to replace equality in a first-order structure with a complete metric built into the language; after all, equality in a way is really just a discrete metric. We then obtain super nice model-theoretic results about metric structures, such as axiomatizablity of Hilbert spaces. Doing so, however, demands a logic the permits continuum many truth values. In this talk, I will introduce continuous logic for metric structures, discuss its semantic properties, and provide a sound-and-complete Hilbert-style proof system. Afterwards, I will talk about my progress in finding a Gentzen-style proof system for continuous logic and difficulties I have encountered. Slides

### April 21

Speaker: 郭予峤 Yuqiao Guo

Time: 12:00 - 13:00. Location: HGW2403.

#### 精致逼真性与近似真

逼真性是由波普尔首创的科学哲学概念，对它的集中研究开始于 70 年代末。在力图对这个概念给出逻辑刻画的过程中，出现了很多不同的句法和语义方案，其丰富程度使得逼真性远远超出了其最初的证伪主义背景，成为一个位于哲学逻辑、形式知识论和科学哲学的交叉领域的研究。在这次报告中，我将介绍由荷兰逻辑学家 Zwart 提出的一种给逼真性定义做分类的方法并且用这种方法来评估一种可能的逼真性定义：精致的近似逼真性。这个定义将试图结合 Weston 的近似真定义和 Zwart 的精致逼真性；最后，我会试图阐明这种逼真性所处的问题层次以及它与一些邻近概念之间的关系。