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].