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

Journal of Symbolic Logic 52 (3):651-664 (1987)
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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Boaz Tsaban (2004). The Combinatorics of Splittability. Annals of Pure and Applied Logic 129 (1-3):107-130.
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