A property of forcing notions and preservation of cardinal invariants

We define a property of forcing notions and show that there exists a model of its forcing axiom and the negation of the continuum hypothesis in which the Cichon-Blass diagram of cardinal invariants is the same as in the Cohen model. As a corollary, its forcing axiom and the forcing axiom for sigma-centered forcing notions are independent of each other.

Automated summary

We define a property of forcing notions and prove the existence of a model in which this property holds and the continuum hypothesis is negated, while the Cichon-Blass diagram of cardinal invariants matches that of the Cohen model. As a consequence, the forcing axiom and the forcing axiom for sigma-centered forcing notions are shown to be independent of each other.