Calculating quotient algebras of generic embeddings

  title={Calculating quotient algebras of generic embeddings},
  author={Matthew D. Foreman},
  journal={Israel Journal of Mathematics},
  • M. Foreman
  • Published 2013
  • Mathematics
  • Israel Journal of Mathematics
Many consistency results in set theory involve forcing over a universe V0 that contains a large cardinal to get a model V1. The original large cardinal embedding is then extended generically using a further forcing by a partial ordering ℚ. Determining the properties of ℚ is often the crux of the consistency result. Standard techniques can usually be used to reduce to the case where ℚ is of the form P(Z)/J for appropriately chosen Z and countably complete ideal J. This paper proves a general… 

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