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June 2004 Ladder gaps over stationary sets
Uri Abraham, Saharon Shelah
J. Symbolic Logic 69(2): 518-532 (June 2004). DOI: 10.2178/jsl/1082418541

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.

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Uri Abraham. Saharon Shelah. "Ladder gaps over stationary sets." J. Symbolic Logic 69 (2) 518 - 532, June 2004. https://doi.org/10.2178/jsl/1082418541

Information

Published: June 2004
First available in Project Euclid: 19 April 2004

zbMATH: 1070.03033
MathSciNet: MR2058187
Digital Object Identifier: 10.2178/jsl/1082418541

Rights: Copyright © 2004 Association for Symbolic Logic

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Vol.69 • No. 2 • June 2004
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