On freedom and independence in hypergraphs of models of theories

Curious properties of free hypergraph C*-algebras

A finite hypergraph $H$ consists of a finite set of vertices $V(H)$ and a collection of subsets $E(H) \subseteq 2^{V(H)}$ which we consider as partition of unity relations between projection operators. These partition of unity relations freely generate a universal C*-algebra, which we call the "free hypergraph C*-algebra" $C^*(H)$. General free hypergraph C*-algebras were first studied in the context of quantum contextuality. As special cases, the class of free hypergraph C*-algebras comprises quantum permutation groups, maximal group C*-algebras of graph products of finite cyclic groups, and …

Conant-独立性与广义自由融合

Conant-independence and generalized free amalgamation

该研究引入并研究Conant-独立性，通过推广自由融合公理刻画其与NSOPₙ层级的关联，证明相关理论的性质分界线，回答了Conant的公开问题，为新稳定性理论提供了新的研究方向。