AI 中文总结
本文证明超简单理论的SU-秩在扩张中非递减，通过构造具有一致分叉模式的树来处理极限秩，并在可数秩情形给出清晰描述。
AI 中文摘要
我们证明了超简单理论的 SU-秩不大于其任何超简单扩张的 SU-秩。有限秩情形的证明已存在于文献中，但非连续性在极限秩处构成问题。我们通过归约到在基础理论中寻找某些分叉扩张的树来逐类型证明 SU-秩在扩张中的非递减性，其中见证分叉的公式和分叉数具有足够一致的模式。在可数秩的情形下，我们可以给出这种一致性的特别清晰的描述：对于可数序数 $\alpha$，超简单理论中任何 SU-秩至少为 $\alpha$ 的类型都具有一个反向序型为 $\alpha$ 的分叉扩张链。
英文摘要
We prove that the SU-rank of a supersimple theory is no greater than that of any of its supersimple expansions. A proof for finite rank theories already exists in the literature, but non-continuity presents a problem at limit ranks. We prove the non-decreasing of SU-rank in expansions type-by-type by reducing to finding, in the base theory, certain trees of forking extensions in which the formulas and dividing numbers which witness dividing have a sufficiently uniform pattern. In the case of countable ranks, we can give an especially nice description of this uniformity: for a countable ordinal $α$, any type of SU-rank at least $α$ in a supersimple theory has a chain of forking extensions in the reverse order type of $α$.
