Journal of Symbolic Logic

Forcing indestructibility of set-theoretic axioms

Bernhard König

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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.

Article information

J. Symbolic Logic, Volume 72, Issue 1 (2007), 349-360.

First available in Project Euclid: 23 March 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E35: Consistency and independence results 03E50: Continuum hypothesis and Martin's axiom [See also 03E57]

Forcing axioms transfer principles


König, Bernhard. Forcing indestructibility of set-theoretic axioms. J. Symbolic Logic 72 (2007), no. 1, 349--360. doi:10.2178/jsl/1174668399.

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