Some remarks on atypical intersections

In this paper we show how some known weak forms of the Zilber--Pink conjecture can be strengthened by combining them with Mordell--Lang or its variants. We illustrate idea proving theorems on atypical intersections in semiabelian and modular settings. Given a "finitely generated" set $\Gamma$ certain structure, consider $\Gamma$-special subvarieties -- weakly special containing point that every variety $V$ contains only finitely many maximal $\Gamma$-atypical subvarieties, i.e. varieties closures which are $\Gamma$-special.