Definable $(\omega ,2)$-theorem for families with VC-codensity less than $2$

Pablo Andújar Guerrero

Let $\mathcal{S}$ be a family of sets with VC-codensity less than $2$. We prove that, if $\mathcal{S}$ has the $(\omega ,2)$-property (for any infinitely many sets in $\mathcal{S}$, at…