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Ladder gaps over stationary sets

Published online by Cambridge University Press:  12 March 2014

Uri Abraham
Department of Mathematics, Ben-Gurion University, Beér-Sheva, 84105, Israel, E-mail:
Saharon Shelah
Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail:


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 ω1S 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.

Research Article
Copyright © Association for Symbolic Logic 2004

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