Cofinal families of finite VC-dimension

Omer Ben-Neria, Itay Kaplan, George Peterzil

Given infinite cardinals $\theta \le \kappa$, we ask for the minimal VC-dimension of a cofinal family $\mathcal{F}\subseteq [\kappa {]}^{<\theta }$. We show that for $\theta =\omega$ and $\kappa ={\aleph }_n$ it is consistent…