Abstract

K.J. Devlin has extended Jensen's construction of a model ofZFC andCH without Souslin trees to a model without Kurepa trees either. We modify the construction again to obtain a model with these properties, but in addition, without Kurepa trees inccc-generic extensions. We use a partially defined ◊-sequence, given by a fine structure lemma. We also show that the usual collapse ofκ Mahlo toω 2 will give a model without Kurepa trees not only in the model itself, but also inccc-extensions