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Pré-Publication, Document De Travail Année : 2006

Forcing indestructibility of set-theoretic axioms

Bernhard Koenig
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Résumé

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 $\aleph_\omega$ not being Jonsson which answers a question raised during Oberwolfach 2005.
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Dates et versions

hal-00023750 , version 1 (04-05-2006)

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Bernhard Koenig. Forcing indestructibility of set-theoretic axioms. 2006. ⟨hal-00023750⟩
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