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math.LO2023
Computability of Countable Sunflowers
Nathanael Ackerman, Leah Karker, Mostafa Mirabi
We provide a characterization of when a countably infinite set of finite sets contains an infinite sunflower. We also show that the collection of such sets is Turing equivalent to…
math.CO2023
Algebraic Sunflowers
Nathanael Ackerman, Mostafa Mirabi
We study sunflowers within the context of finitely generated substructures of ultrahomogeneous structures. In particular, we look at bounds on how large a set system is needed to g…
math.LO2023
Asymptotic Classes of Trees and -categoricity
Mostafa Mirabi
This paper focuses on the characterization of -categorical theories of trees in the following sense: for any -cateorical theory of trees there is a tree pla…