Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-13T00:34:40.714Z Has data issue: false hasContentIssue false
  • English
  • Français

Ladder gaps over stationary sets

Published online by Cambridge University Press:  12 March 2014

Uri Abraham  and
Saharon Shelah
Uri Abraham
Affiliation:
Department of Mathematics, Ben-Gurion University, Beér-Sheva, 84105, Israel, E-mail: [email protected]
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract.

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 2 , June 2004 , pp. 518 - 532
Copyright
Copyright © Association for Symbolic Logic 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

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