Colouring homogeneous structures

2020/08/05 by Norbert Sauer, Sauer, Norbert
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2008.02375

openalex publication_date 2020/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A relational structure is indivisible if for every partition of its set of elements into two parts there exists an embedding of the structure into one of the parts of the partition. A relational structure is homogeneous if every embedding of a finite induced substructure to a finite induced substructure extends to an automorphism. This article establishes a necessary and sufficient condition for Henson type, see [4], homogeneous structures to be indivisible.

Citations

• The poset of copies for automorphism groups of countable relational structures

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