## Journal of Symbolic Logic

### Ladder gaps over stationary sets

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 19 April 2004

https://projecteuclid.org/euclid.jsl/1082418541

Digital Object Identifier
doi:10.2178/jsl/1082418541

Mathematical Reviews number (MathSciNet)
MR2058187

Zentralblatt MATH identifier
1070.03033

#### Citation

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

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