Class Forcing in Class Theory

@article{Antos2018ClassFI,
  title={Class Forcing in Class Theory},
  author={Carolin Antos},
  journal={arXiv: Logic},
  year={2018},
  pages={1-16}
}
  • C. Antos
  • Published 28 February 2015
  • Mathematics
  • arXiv: Logic
In this article we show that Morse-Kelley class theory (MK) provides us with an adequate framework for class forcing. We give a rigorous definition of class forcing in a model \((M,\mathcal {C})\) of MK, the main result being that the Definability Lemma (and the Truth Lemma) can be proven without restricting the notion of forcing. Furthermore we show under which conditions the axioms are preserved. We conclude by proving that Laver’s Theorem does not hold for class forcings. 
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