Ladder Gaps over Stationary Sets

Journal of Symbolic Logic 69 (2):518 - 532 (2004)
  Copy   BIBTEX

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} \ 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

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,127

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Splitting stationary sets in.Toshimichi Usuba - 2012 - Journal of Symbolic Logic 77 (1):49-62.
Applications of cohomology to set theory I: Hausdorff gaps.Daniel E. Talayco - 1995 - Annals of Pure and Applied Logic 71 (1):69-106.
Isols and maximal intersecting classes.Jacob C. E. Dekker - 1993 - Mathematical Logic Quarterly 39 (1):67-78.
Full reflection at a measurable cardinal.Thomas Jech & Jiří Witzany - 1994 - Journal of Symbolic Logic 59 (2):615-630.
A weak variation of Shelah's I[ω₂].William J. Mitchell - 2004 - Journal of Symbolic Logic 69 (1):94-100.
Local saturation of the non-stationary ideal over Pκλ.Toshimichi Usuba - 2007 - Annals of Pure and Applied Logic 149 (1-3):100-123.
Projective Hausdorff gaps.Yurii Khomskii - 2014 - Archive for Mathematical Logic 53 (1-2):57-64.
Nonsplitting subset of κ.Moti Gitik - 1985 - Journal of Symbolic Logic 50 (4):881-894.
Stationary Cardinals.Wenzhi Sun - 1993 - Archive for Mathematical Logic 32 (6):429-442.

Analytics

Added to PP
2010-08-24

Downloads
50 (#327,457)

6 months
11 (#272,000)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Internal cohen extensions.D. A. Martin & R. M. Solovay - 1970 - Annals of Mathematical Logic 2 (2):143-178.
Applications of cohomology to set theory I: Hausdorff gaps.Daniel E. Talayco - 1995 - Annals of Pure and Applied Logic 71 (1):69-106.

Add more references