We show that (a) PFA is consistent with having that NS_{\omega_1} is \Pi_1 definable and that (b) MM proves that NS_{\omega_1} is not \Pi_1 definable. Yet another time this shows that MM is the right generalization of MA. This is joint work with D. Asperó, S. Hoffelner, P. Larson, X. Sun, L. Wu.