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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

REFERENCES

[B1] Balcar, B., Pelant, J., and Simon, P., The space of ultrafilters on N covered by nowhere dense sets, fundament a Mathematicae, vol. 110 (1980), pp. 11–24.CrossRefGoogle Scholar
[B2] Baumgartner, J., Iterated forcing, Surveys in set theory (Mathias, A.R.D., editor), London Mathematical Society Lecture Note Series, no. 87, Cambridge University Press, Cambridge, 1983, pp. 1–59.Google Scholar
[B3] Baumgartner, J. and Dordal, P., Adjoining dominating functions, this Journal, vol. 50 (1985), pp. 94–101.Google Scholar
[D1] Dordal, P., Independence results concerning some combinatorial properties of the continuum, Ph.D. Dissertation, Harvard University, Cambridge, Massachusetts, 1982.Google Scholar
[D2] van Douwen, E., The integers and topology, The handbook of set-theoretic topology (Kunen, K. and Vaughan, J., editors), North-Holland, Amsterdam, 1984, pp. 111–167.CrossRefGoogle Scholar
[D3] Dow, A., Tree Π-bases for βN – N in various models (to appear).Google Scholar
[H] Hausdorff, F., Summenvon ℵ1 Mengen, Fundamenta Mathematicae, vol. 26 (1936), pp. 241–255.CrossRefGoogle Scholar
[J] Jech, T., Set theory, Academic Press, New York, 1978.Google Scholar
[L] Laver, R., On the consistency of Borel's conjecture, Acta Mathematica, vol. 137 (1976), 151–169.Google Scholar
[M] Mitchell, W., Aronszajn trees and the independence of the transfer property, Annals of Mathematical Logic, vol. 5 (1972), pp. 21–46.CrossRefGoogle Scholar