# Sh:598

- Abraham, U., & Shelah, S. (2004).
*Ladder gaps over stationary sets*. J. Symbolic Logic,**69**(2), 518–532. arXiv: math/0404151 DOI: 10.2178/jsl/1082418541 MR: 2058187 -
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. - 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}, doi = {10.2178/jsl/1082418541}, mrclass = {03E35 (03E05)}, mrnumber = {2058187}, mrreviewer = {P\'eter Komj\'ath}, doi = {10.2178/jsl/1082418541}, note = {\href{https://arxiv.org/abs/math/0404151}{arXiv: math/0404151}}, arxiv_number = {math/0404151} }