A property of forcing notions and preservation of cardinal invariants

Abstract

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 Cichoń‐Blass diagram of cardinal invariants is the same as in the Cohen model. As a corollary, its forcing axiom and the forcing axiom for σ‐centered forcing notions are independent of each other.