Forcing axioms and construction schemes

Source abstract

We continue the development of the theory of construction schemes over [Formula: see text] as introduced by the third author by studying their relation with forcing axioms. Formally, we introduce the cardinals [Formula: see text] and use the consistency of [Formula: see text] to prove a fundamental result relating gaps and almost disjoint families over [Formula: see text]. The cardinals [Formula: see text] are also used to prove some delimitative results for construction schemes, some of which answer questions from the previous literature. Finally, we show that PID implies the non-existence of 2-capturing schemes.