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March 2007 Forcing indestructibility of set-theoretic axioms
Bernhard König
J. Symbolic Logic 72(1): 349-360 (March 2007). DOI: 10.2178/jsl/1174668399

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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Bernhard König. "Forcing indestructibility of set-theoretic axioms." J. Symbolic Logic 72 (1) 349 - 360, March 2007. https://doi.org/10.2178/jsl/1174668399

Information

Published: March 2007
First available in Project Euclid: 23 March 2007

zbMATH: 1128.03043
MathSciNet: MR2298486
Digital Object Identifier: 10.2178/jsl/1174668399

Subjects:
Primary: 03E35, 03E50

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 1 • March 2007
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