English

Forcing indestructibility of set-theoretic axioms

Logic 2007-05-23 v1

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

Keywords

Cite

@article{arxiv.math/0605129,
  title  = {Forcing indestructibility of set-theoretic axioms},
  author = {Bernhard Koenig},
  journal= {arXiv preprint arXiv:math/0605129},
  year   = {2007}
}
R2 v1 2026-07-22T17:35:23.280Z