Type: Article

Forcing properties of Boolean algebras of the type P (w)/I

Campero-Arena, G., Guzman-Gonzalez, O., Hrusak. M., Meza-Alcantara, D.;

Abstract:

We study forcing properties of the Boolean algebras P(?)/I, where I is a Borel ideal on ?. We show (Theorem 2.12) that (under a large cardinal hypothesis) P(?)/I does not add reals if and only if it has a dense ?-closed subset. For analytic P-ideals I we show (Theorem 3.3) that either P(?)/I is ??-bounding or it is not proper. We also investigate the existence of completely separable I-MAD families.