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Forcing indestructibility of set-theoretic axioms

Published online by Cambridge University Press:  12 March 2014

Bernhard KÖnig
Bernhard KÖnig*
Affiliation:
UniversitÉ Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, France Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 2E4, Canada. E-mail: bkoenig@math.toronto.edu
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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.

Keywords

Forcing axiomstransfer principles
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 1 , March 2007 , pp. 349 - 360
Copyright
Copyright © Association for Symbolic Logic 2007

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