Harvey Friedman’s gap condition on embeddings of finite labelled trees plays an important role in combinatorics (proof of the graph minor theorem) and mathematical logic (strong independence results). In the present paper we show that the gap condition can be reconstructed from a small number of well-motivated building blocks: It arises via iterated applications of a uniform Kruskal theorem.

中文翻译：

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从克鲁斯卡尔定理到弗里德曼的间隙条件

哈维弗里德曼关于有限标记树嵌入的间隙条件在组合学（图小定理的证明）和数学逻辑（强独立性结果）中起着重要作用。在本文中，我们展示了间隙条件可以从少量动机良好的构建块中重建：它是通过统一 Kruskal 定理的迭代应用而产生的。