Dividing and forking in random hypergraphs
Hirotaka Kikyo, Akito Tsuboi · Annals of Pure and Applied Logic · 2024
We investigate the class of m -hypergraphs in which substructures with l elements have more than s subsets of size m that do not form a hyperedge. The class has a (unique) Fraïssé limit, if 0 ≤ s < ( l − 2 m − 2 ) . We show that the theory of the Fraïssé limit has SU -rank one if 0 ≤ s < ( l − 3 m − 3 ) , and dividing and forking will be different concepts in the theory if ( l − 3 m − 3 ) ≤ s < ( l − 2 m − 2 ) .