# Calculating quotient algebras of generic embeddings

@article{Foreman2013CalculatingQA, title={Calculating quotient algebras of generic embeddings}, author={Matthew D. Foreman}, journal={Israel Journal of Mathematics}, year={2013}, volume={193}, pages={309-341} }

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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