naa a22 4500 510782434 CHVBK 20180411083252.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s11856-012-0118-9 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0118-9 Foreman Matthew Department of Mathematics, University of California at Irvine, 92697-3875, Irvine, CA, USA aut Calculating quotient algebras of generic embeddings [Elektronische Daten] [Matthew Foreman] Many consistency results in set theory involve forcing over a universe V 0 that contains a large cardinal to get a model V 1. 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 algebraic Duality Theorem that exactly characterizes the Boolean algebra P(Z)/J. The Duality Theorem is general enough that it applies even if the original embedding in V 0 was itself generic. Thus it has as corollaries the theorems of Kakuda, Baumgartner, Laver and others about preservation properties of precipitous and saturated ideals. A corollary is drawn showing that precipitous ideals are indestructible under small proper forcing. Hebrew University Magnes Press, 2012 Israel Journal of Mathematics The Hebrew University Magnes Press 193/1(2013-01-01), 309-341 0021-2172 193:1<309 2013 193 11856 https://doi.org/10.1007/s11856-012-0118-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0118-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Foreman Matthew Department of Mathematics, University of California at Irvine, 92697-3875, Irvine, CA, USA aut NATIONALLICENCE 773 0- Israel Journal of Mathematics The Hebrew University Magnes Press 193/1(2013-01-01), 309-341 0021-2172 193:1<309 2013 193 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer