In this paper we isolate the notion of Stratified class forcing and show that Stratification implies cofinality-preservation and is preserved by iterations with the appropriate support. Many familiar class forcings are stratified and therefore can be simultaneously iterated without changing cofinalities, provided the proper support is used. Easton forcing, Backward Easton forcings and some modifications of Jensen coding are stratified. Jensen coding is not stratified but instead obeys a related… Expand

We prove that it is consistent relative to a Mahlo cardinal that all sets of reals definable from countable sequences of ordinals are Lebesgue measurable, but at the same time, there is a… Expand

It is shown that if a class forcing amenable to L (an L-forcing) has a generic then it has one definable in a set-generic extension of L[O # ], and that for any countable ordinal α there is an L- forcing which has generics but none periodic of period ≤ α.Expand

Wir zeigen ausgehend von der Konsistenzstarke einer Mahlo-Kardinalzahl dass es konistent ist dass alle projektiven Mengen reeller Zahlen messbar sind, wahrend jedoch eine \Delta^1_3 Menge ohne die… Expand