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Jun 17, 2021 at 8:22 vote accept Dominic van der Zypen
Jun 15, 2021 at 8:53 comment added KP Hart Hope springs eternal but this particular example is tied very strongly to the geometry of the binary tree and it very much uses that both families have the same szie: $\mathfrak{c}$. But maybe you can take an AD family without $3$-element sunflowers and embed it into a binary tree (each member into its own branch).
Jun 15, 2021 at 8:34 comment added Joel David Hamkins Is there any hope to modify the construction to work with an arbitrary almost disjoint family that is maximal with respect to not including 3-element sunflowers? This would lead to an answer to my question at mathoverflow.net/q/394987/1946.
Jun 15, 2021 at 7:23 history edited Joel David Hamkins CC BY-SA 4.0
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Jun 15, 2021 at 7:20 comment added KP Hart Indeed. Thanks.
Jun 15, 2021 at 7:20 history edited KP Hart CC BY-SA 4.0
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Jun 14, 2021 at 21:49 history answered KP Hart CC BY-SA 4.0