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Exactly two and exactly three near-coherence classes
Journal of Mathematical Logic 24 (1) (2023)
Abstract
We prove that for [Formula: see text] and [Formula: see text] there is a forcing extension with exactly n near-coherence classes of non-principal ultrafilters. We introduce localized versions of Matet forcing and we develop Ramsey spaces of names. The evaluation of some of the new forcings is based on a relative of Hindman’s theorem due to Blass 1987.Links
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References found in this work
Set Theory. An Introduction to Independence Proofs.James E. Baumgartner & Kenneth Kunen - 1986 - Journal of Symbolic Logic 51 (2):462.
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.
Near coherence of filters. I. Cofinal equivalence of models of arithmetic.Andreas Blass - 1986 - Notre Dame Journal of Formal Logic 27 (4):579-591.
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