Cofinal families of finite VC-dimension

Omer Ben-Neria, Itay Kaplan, George Peterzil

Given infinite cardinals $\hat{I}¸\le \hat{I}º$, we ask for the minimal VC-dimension of a cofinal family $\mathcal{F}\subseteq [\hat{I}º{]}^{<\hat{I}¸}$. We show that for $\hat{I}¸=\ddot{I}‰$ and $\hat{I}º={\aleph }_n$ it is con…