Ladder gaps over stationary sets

Abraham, Uri; Shelah, Saharon

J. Symbolic Logic, Tome 69 (2004) no. 1, p. 518-532 / Harvested from Project Euclid

Résumé

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.

Publié le : 2004-06-15
Classification:

@article{1082418541,
     author = {Abraham, Uri and Shelah, Saharon},
     title = {Ladder gaps over stationary sets},
     journal = {J. Symbolic Logic},
     volume = {69},
     number = {1},
     year = {2004},
     pages = { 518-532},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1082418541}
}

Abraham, Uri; Shelah, Saharon. Ladder gaps over stationary sets. J. Symbolic Logic, Tome 69 (2004) no. 1, pp.  518-532. http://gdmltest.u-ga.fr/item/1082418541/