Ladder gaps over stationary sets

Uri Abraham; Saharon Shelah

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Ladder gaps over stationary sets

Uri Abraham·Saharon Shelah

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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 setminus 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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BibTeX RIS

Uri Abraham, Saharon Shelah. 2004-04-07. Ladder gaps over stationary sets. https://arxiv.org/abs/math/0404151

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