Extensive embeddings into Fraïssé structures and stationary weak independence relations

Abstract: Let $M$ be a Fra\"{i}ss\'{e} structure (a countably infinite ultrahomogeneous structure). We call an embedding $f : A \to M$ extensive if each automorphism of its image extends to an automorphism of $M$, where the extension map respects composition. We consider which Fra\"{i}ss\'{e} structures $M$ have the property that each substructure admits an extensive embedding into $M$. We also consider which Fra\"{i}ss\'{e} structures have a stationary weak independence relation (SWIR) as defined by Li, and discuss the relationship between SWIRs and extensive embeddings.