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Finding generic filters by playing games
Archive for Mathematical Logic 49 (1):91-118 (2010)
Abstract
We give some restrictions for the search for a model of the club principle with no Souslin trees. We show that ${\diamondsuit(2^\omega, [\omega]^\omega}$ , is almost constant on) together with CH and “all Aronszajn trees are special” is consistent relative to ZFC. This implies the analogous result for a double weakening of the club principleMy notes
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References found in this work
There may be simple Pℵ1 and Pℵ2-points and the Rudin-Keisler ordering may be downward directed.Andreas Blass & Saharon Shelah - 1987 - Annals of Pure and Applied Logic 33 (C):213-243.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
A Δ22 well-order of the reals and incompactness of L.Uri Abraham & Saharon Shelah - 1993 - Annals of Pure and Applied Logic 59 (1):1-32.
Near coherence of filters. III. A simplified consistency proof.Andreas Blass & Saharon Shelah - 1989 - Notre Dame Journal of Formal Logic 30 (4):530-538.
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