Structured Sunflowers
Nathanael Ackerman, Mary Leah Karker, Mostafa Mirabi

TL;DR
This paper introduces the concept of sunflowerability in infinite structures, providing conditions for it, characterizing certain structures, and exploring related properties like indivisibility and the sunflower property of ages.
Contribution
It establishes sufficient conditions for sunflowerability, characterizes countable linear orderings that are sunflowerable, and links sunflowerability to indivisibility and properties of ages.
Findings
Several well-known structures are shown to be sunflowerable.
A complete characterization of countable linear orderings that are sunflowerable.
Sunflowerable structures must be indivisible, with implications for Fra"issé limits.
Abstract
We call an infinite structure sunflowerable if whenever is isomorphic to with underlying set , consisting of finite sets of bounded size, there is an such that is a sunflower and is isomorphic to . We give sufficient conditions on to show that is sunflowerable. These conditions allow us to show that several well-known structures are sunflowerable and give a complete characterization of the countable linear orderings which are sunflowerable. We show that a sunflowerable structure must be indivisible. This allows us to show that any Fra\"iss\'e limit which has the 3-disjoint amalgamation property and a single unary type must be indivisible. In addition to studying sunflowerability of infinite structures, we also consider an analogous…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
