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arXiv:math/0404151 [math.LO]AbstractReferencesReviewsResources

Ladder gaps over stationary sets

Uri Abraham, Saharon Shelah

Published 2004-04-07Version 1

For a stationary set S subseteq omega_1 and a ladder system C over S, a new type of gaps called C-Hausdorff is introduced and investigated. We describe a forcing model of ZFC in which, for some stationary set S, for every ladder C over S, every gap contains a subgap that is C-Hausdorff. But for every ladder E over omega_1 setminus S there exists a gap with no subgap that is E-Hausdorff. A new type of chain condition, called polarized chain condition, is introduced. We prove that the iteration with finite support of polarized c.c.c posets is again a polarized c.c.c poset.

Categories: math.LO
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