Fudan Logic Student Seminar 2026
June 26
Speaker: 曾柏翔 ZENG, Boxiang
Time: 13:30 - 14:30. Location: HGW2403.
From Proofs and Refutations to Constitutive Reconstruction: Applying and Refining the Lakatosian Framework through the Early History of Set Theory
Lakatos's Proofs and Refutations offers an influential dialectical model of mathematical knowledge growth, yet it is constructed almost entirely from a single case. This report tests the Lakatosian framework against a structurally different case: the early history of set theory from Cantor to ZFC. Three systematic limitations are identified during this test. To solve these problems, a three-layer analytical framework is constructed, integrating the theory of Lakatos, Cellucci and the theoretical insights from the set-theory case. At last, some dialogues between the framework and other alternative theory will be taken.
Speaker: 车晓舟 CHE, Xiaozhou
Time: 14:30 - 15:30. Location: HGW2403.
Type-definable subgroups and f-generic types of 1D algebraic groups over RCVF
In model theory, the classification of algebraic groups and their definable subgroups over valued fields is an important research topic. Building upon the recent complete classification over algebraically closed valued fields (ACVF) by Acosta and Hils, the study extends the context to real closed valued fields (RCVF). By utilizing model-theoretic tools such as the weak o-minimality of RCVF and opaque maps, we study type-definable subgroups of four one-dimensional algebraic groupss.Furthermore, we analyze the 1-type spaces of $K_1 = \mathbb{R}((t))$ and $K_2 = \mathbb{R}((t^\mathbb{Q}))$.
Speaker: 陈婧仪 CHEN, Jingyi
Time: 15:30 - 16:30. Location: HGW2403.
O-minimal Fundamental Group, Homology and Manifolds
In this presentation, I will discuss the paper O-minimal Fundamental Group, Homology and Manifolds by Alessandro Berarducci and Margarita Otero. The paper develops fundamental notions of algebraic topology within the framework of o-minimal structures, extending classical topological concepts to the category of definable sets and definable manifolds.
The main objective of the paper is to establish o-minimal analogues of the fundamental group, homology groups, and manifold theory. Starting from the geometric tameness provided by cell decomposition and definable triangulation, the authors introduce definable paths and homotopies, construct the o-minimal fundamental group, and develop a homology theory satisfying the standard Eilenberg–Steenrod axioms. These tools allow many classical results of algebraic topology to be recovered in the o-minimal setting.
Particular attention will be given to the construction of o-minimal homology and its relationship with triangulation theory, as these ideas provide the foundation for defining topological invariants such as the Euler characteristic. The presentation will also explain how the theory of definable manifolds fits naturally into this framework and why these developments are important for further results in tame topology and model theory.
The goal of the talk is to present the main results of the paper, and to highlight the mathematical intuition behind transferring algebraic topology from classical spaces to definable spaces.
March 20
Speaker: 陈俊宏 CHEN, Junhong
Time: 13:30 - 15:00. Location: HGW2403.
The Coding Conception of Set
This report focuses on a new Conception of Set developed in current research. This Conception takes ordinals as prior to sets and maintains that set theory ought to be regarded as a consequence of ordinal theory. Specifically, we argue that $\mathsf{ZFGC}$ is in fact a true first-order ordinal theory, while the true second-order ordinal theory admits three possible directions of divergence. Each of these directions offers a distinct prediction concerning the shape of the true set-theoretic universe: the $\mathsf{ZFGC}^2$ single universe, the countabilist single universe, and a new maximal single universe constructed from a multiverse perspective, which we refer to as the coding multiverse. By conducting technical derivations on the potential of the strengthened theories associated with these three possible directions, combined with philosophical arguments, we demonstrate that the third type of universe is sufficiently justified to be accepted, thereby proposing a new set-theoretic worldview. Finally, we briefly outline prospects for the possible Gödel Program within this worldview.