A model in which the base-matrix tree cannot have cofinal branches

Journal of Symbolic Logic 52 (3):651-664 (1987)
Abstract
A model of ZFC is constructed in which the distributivity cardinal h is 2 ℵ 0 = ℵ 2 , and in which there are no ω 2 -towers in [ω] ω . As an immediate corollary, it follows that any base-matrix tree in this model has no cofinal branches. The model is constructed via a form of iterated Mathias forcing, in which a mixture of finite and countable supports is used
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DOI 10.2307/2274354
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Towers in [Ω]Ω and Ωω.Peter Lars Dordal - 1989 - Annals of Pure and Applied Logic 45 (3):247-276.
The Combinatorics of Splittability.Boaz Tsaban - 2004 - Annals of Pure and Applied Logic 129 (1-3):107-130.

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