Forcing indestructibility of set-theoretic axioms

Bernhard Koenig

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Forcing indestructibility of set-theoretic axioms

Bernhard Koenig

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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 Levy-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 $\aleph\_1$. Later we give applications, among them the consistency of ${\rm MM}$ with $\aleph\_ω$ not being Jonsson which answers a question raised during Oberwolfach 2005.

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Bernhard Koenig. 2006-05-04. Forcing indestructibility of set-theoretic axioms. https://arxiv.org/abs/math/0605129

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