# Sh:598

• Abraham, U., & Shelah, S. (2004). Ladder gaps over stationary sets. J. Symbolic Logic, 69(2), 518–532.
• 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.
• Current version: 2002-07-31_11 (21p) published version (16p)
Bib entry
@article{Sh:598,
author = {Abraham, Uri and Shelah, Saharon},
title = {{Ladder gaps over stationary sets}},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {69},
number = {2},
year = {2004},
pages = {518--532},
issn = {0022-4812},
mrnumber = {2058187},
mrclass = {03E35 (03E05)},
doi = {10.2178/jsl/1082418541},
note = {\href{https://arxiv.org/abs/math/0404151}{arXiv: math/0404151}},
arxiv_number = {math/0404151}
}