Ladder gaps over stationary sets
Logic
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0404151,
title = {Ladder gaps over stationary sets},
author = {Uri Abraham and Saharon Shelah},
journal= {arXiv preprint arXiv:math/0404151},
year = {2007}
}