Group-extensive embeddings into Fraïssé structures and stationary weak independence relations

Aleksandra Kwiatkowska; Rob Sullivan; Jeroen Winkel

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arXiv · 2508.06370

Group-extensive embeddings into Fraïssé structures and stationary weak independence relations

Aleksandra Kwiatkowska·Rob Sullivan·Jeroen Winkel

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Abstract

Let $M$ be a Fraïssé structure (a countably infinite ultrahomogeneous structure). We call an embedding $f : A \to M$ group-extensive if each automorphism of its image extends to an automorphism of $M$, where the extension map respects composition. We say that $M$ has group-extensible $ω$-age if each substructure admits a group-extensive embedding into $M$. We investigate the relationship between the following two properties: the presence of a stationary weak independence relation (SWIR) on $M$, and group-extensibility of the $ω$-age of $M$. We show that linearly ordered Fraïssé structures with a SWIR have group-extensible $ω$-age, but also we give examples of Fraïssé structures where only one of the two properties holds. Finally, we consider whether a wide range of examples of Fraïssé structures have group-extensible $ω$-age or a finite SWIR expansion, including all countably infinite ultrahomogeneous oriented graphs (with one exception).

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BibTeX RIS

Aleksandra Kwiatkowska, Rob Sullivan, Jeroen Winkel. 2026-08-06. Group-extensive embeddings into Fraïssé structures and stationary weak independence relations. https://arxiv.org/abs/2508.06370

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