Assume I define $$ m_G = \bigcup \{ s \in fin(\omega) \mid \exists x \in \mathcal{U}((s,x) \in G) \}$$ where G is an $\mathbb{M}_\mathcal{U}$-generic filter and
$$ M_\mathcal{U} = \{ (s,x) \mid s \in fin(\omega) \land x \in \mathcal{U} \land \max(s) < \min(x) \}$$ and
$$ (s,x) \leq (t,y) \iff s \subseteq t \land y \subseteq x \land t \setminus s \subseteq x$$