Journal of Symbolic Logic 72 (1):349 - 360 (2007)

Abstract
Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Lévy collapse. These show in particular that certain applications of forcing axioms require to add generic countable sequences high up in the set-theoretic hierarchy even before collapsing everything down to ‮א‬₁. Later we give applications, among them the consistency of MM with ‮א‬ω not being Jónsson which answers a question raised in the set theory meeting at Oberwolfach in 2005
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DOI 10.2178/jsl/1174668399
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References found in this work BETA

[Omnibus Review].Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.
Set Mapping Reflection.Justin Tatch Moore - 2005 - Journal of Mathematical Logic 5 (1):87-97.
Bounded Forcing Axioms as Principles of Generic Absoluteness.Joan Bagaria - 2000 - Archive for Mathematical Logic 39 (6):393-401.

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Citations of this work BETA

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