We prove canonical and non-canonical tree-of-tangles theorems for abstract separation systems that are merely structurally submodular. Our results imply all known tree-of-tangles theorems for graphs, matroids and abstract separation systems with submodular order functions, with greatly simplified and shortened proofs.

中文翻译：

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抽象分离系统中的缠结树

我们证明了仅在结构上是亚模的抽象分离系统的规范和非规范的缠结树定理。我们的结果暗示了所有已知的带有次模阶函数的图，拟阵和抽象分离系统的缠结树定理，并大大简化和缩短了证明。