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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 usedLinks
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Citations of this work
Special ultrafilters and cofinal subsets of $$({}^omega omega, <^*)$$.Peter Nyikos - 2020 - Archive for Mathematical Logic 59 (7-8):1009-1026.
Games on Base Matrices.Vera Fischer, Marlene Koelbing & Wolfgang Wohofsky - 2023 - Notre Dame Journal of Formal Logic 64 (2):247-251.
The combinatorics of splittability.Boaz Tsaban - 2004 - Annals of Pure and Applied Logic 129 (1-3):107-130.
Property {(hbar)} and cellularity of complete Boolean algebras.Miloš S. Kurilić & Stevo Todorčević - 2009 - Archive for Mathematical Logic 48 (8):705-718.
References found in this work
Aronszajn trees and the independence of the transfer property.William Mitchell - 1972 - Annals of Mathematical Logic 5 (1):21.
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