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From Kruskal’s theorem to Friedman’s gap condition
Anton Freund
Journal:

Mathematical Structures in Computer Science / Volume 30 / Issue 8 / September 2020

Published online by Cambridge University Press:

29 January 2021, pp. 952-975
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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.

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From Kruskal’s theorem to Friedman’s gap condition