TY - JOUR
T1 - Ladder gaps over stationary sets
AU - Abraham, Uri
AU - Shelah, Saharon
PY - 2004/6
Y1 - 2004/6
N2 - For a stationary set S ⊆ ω1 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 ω1 / 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.
AB - For a stationary set S ⊆ ω1 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 ω1 / 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.
UR - http://www.scopus.com/inward/record.url?scp=2942638185&partnerID=8YFLogxK
U2 - 10.2178/jsl/1082418541
DO - 10.2178/jsl/1082418541
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AN - SCOPUS:2942638185
SN - 0022-4812
VL - 69
SP - 518
EP - 532
JO - Journal of Symbolic Logic
JF - Journal of Symbolic Logic
IS - 2
ER -