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Local Clubs, Reflection, and Preserving Stationary Sets
Author(s) -
Feng Qi,
Jech Thomas
Publication year - 1989
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-58.2.237
Subject(s) - mathematics , reflection (computer programming) , computer science , programming language
We introduce the filter of locally closed unbounded sets and investigate its properties. As one application, we give a characterization of forcing notions that preserve stationary sets (in ω 1 ). Also the local club filter and its variants lead to reflection principles for stationary sets. While the general reflection principle is related to Martin's Maximum of Foreman, Magidor and Shelah, the reflection at ω 2 is equiconsistent with a weakly compact cardinal.