论反基础公理模型的双成员图

Undirecting membership in models of ZFA

It is known that, if we take a countable model of Zermelo--Fraenkel set theory ZFC and "undirect" the membership relation (that is, make a graph by joining $x$ to $y$ if either $x\in y$ or $y\in x$), we obtain the Erdős--Rényi random graph. The crucial axiom in the proof of this is the Axiom of Foundation, so it is natural to wonder what happens if we delete this axiom, or replace it by an alternative (such as Aczel's Anti-Foundation Axiom). The resulting graph may fail to be simple, it may have loops (if $x\in x$ for some $x$) or multiple edges (if $x\in y$ and $y\in x$ for some $x,y$). We sh…

通过比较集合的同一性条件来比较反基础公理

Comparing Anti-foundation Axioms by Comparing Identity Conditions for Sets

针对非良基集合论中哪条反基础公理具有哲学合理性的问题，本文提出先确定合理的集合同一性条件、再据此证成对应反基础公理的通用研究路径，并详细分析了两种具合理性的集合同一性条件。

一种新型的反基础公理

A new kind of anti-foundation axioms

本文在四个反基础公理的基础上，将正则互模拟下的反基础公理AFA~推广至具有集合性质的正则互模拟情形，证明该推广可构造出新的反基础公理，具有实质性意义。

The foundation axiom and elementary self-embeddings of the universe

We consider the role of the foundation axiom and various anti-foundation axioms in connection with the nature and existence of elementary self-embeddings of the set-theoretic universe.

超超图与混元图神经网络的理论基础

Theoretical Foundations of Superhypergraph and Plithogenic Graph Neural Networks

本书提出超超图与混元图神经网络的理论框架，旨在扩展信息传递原理以处理高阶结构，通过严谨定义和属性证明，提升复杂网络建模能力。

终端余代数与同伦类型理论中的非良基础集

Terminal Coalgebras and Non-wellfounded Sets in Homotopy Type Theory

本文在同伦类型理论中构建了非良基础集模型，提出扩展AFA和SAFA的通用化，并通过M型构建了满足SAFA通用化的层级模型，同时刻画了M型的身份类型。