Journal of Symbolic Logic

Ladder gaps over stationary sets

Uri Abraham and Saharon Shelah

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

J. Symbolic Logic, Volume 69, Issue 2 (2004), 518-532.

First available in Project Euclid: 19 April 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Abraham, Uri; Shelah, Saharon. Ladder gaps over stationary sets. J. Symbolic Logic 69 (2004), no. 2, 518--532. doi:10.2178/jsl/1082418541.

Export citation


  • S. H. Hechler Short nested sequences in $\beta N \setminus N$ and small maximal almost disjoint families, General Topology and its Applications, vol. 2 (1972), pp. 139--149.
  • D. A. Martin and R. Solovay Internal Cohen extensions, Annals of Mathematical Logic, vol. 2 (1970), pp. 143--178.
  • M. Scheepers Gaps in $\omega^\omega$, Set Theory of the Reals, Israel Mathematical Conference Proceedings (Ramat Gan, 1991), vol. 6, Bar-Ilan University, Ramat Gan,1993, pp. 439--561.
  • D. Talayaco Applications of cohomology to set theory I. Hausdorff gaps, Annals of Pure and Applied Logic, vol. 71 (1995), no. 1, pp. 69--106.