CLASS FORCING, THE FORCING THEOREM AND BOOLEAN COMPLETIONS

@article{Holy2016CLASSFT,
  title={CLASS FORCING, THE FORCING THEOREM AND BOOLEAN COMPLETIONS},
  author={Peter Holy and Regula Krapf and Philipp L{\"u}cke and Ana Njegomir and Philipp Schlicht},
  journal={The Journal of Symbolic Logic},
  year={2016},
  volume={81},
  pages={1500 - 1530}
}
Abstract The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a condition in the relevant generic filter. We show that both the definability (and, in fact, even the amenability) of the forcing relation and the truth lemma can fail for class forcing. In addition to these negative results, we show that the forcing… 
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