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

Published online by Cambridge University Press:  12 March 2014

Peter Lars Dordal
Peter Lars Dordal*
Affiliation:
Department of Mathematics, Loyola University of Chicago, Chicago, Illinois 60626
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Abstract

A model of ZFC is constructed in which the distributivity cardinal h is , 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 3 , September 1987 , pp. 651 - 664
Copyright
Copyright © Association for Symbolic Logic 1987

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References

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