Iterated Class Forcing

@article{Friedman1993IteratedCF,
  title={Iterated Class Forcing},
  author={Sy-David Friedman},
  journal={Mathematical Research Letters},
  year={1993},
  volume={1},
  pages={427-436}
}
  • S. Friedman
  • Published 8 November 1993
  • Environmental Science
  • Mathematical Research Letters
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… 
3 Citations
Easton supported Jensen coding and projective measure without projective Baire
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Generic Saturation
TLDR
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.
Projective Measure Without Projective Baire
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

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