Abstract

We introduce the notion of effective Axiom A and use it to show that some popular tree forcings are Suslin+. We introduce transitive nep and present a simplified version of Shelah’s “preserving a little implies preserving much”: If I is a Suslin ccc ideal (e.g. Lebesgue-null or meager) and P is a transitive nep forcing (e.g. P is Suslin+) and P does not make any I-positive Borel set small, then P does not make any I-positive set small