Ladder Gaps over Stationary Sets

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

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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.

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