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From Kruskal’s theorem to Friedman’s gap condition

Published online by Cambridge University Press:  29 January 2021

Anton Freund Open the ORCID record for Anton Freund [Opens in a new window]
Anton Freund*
Affiliation:
Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany
*
*Corresponding author. Email: freund@mathematik.tu-darmstadt.de
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Abstract

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.

Keywords

Kruskal’s theoremFriedman’s gap conditionlabelled treeswell partial ordersdilators-comprehension
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Issue 8 , September 2020 , pp. 952 - 975
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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