Consistent and inconsistent generalizations of Martin’s Axiom, weak square and weak Chang’s Conjecture

We prove that the forcing axiom Formula: see text (stratified) implies Formula: see text. Using this implication, we show that the forcing axiom Formula: see text is inconsistent. We also derive weak Chang’s Conjecture from Formula: see text (stratified) and use this second implication to give another proof of the inconsistency of Formula: see text.