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On a problem of C. H. Dowker

Published online by Cambridge University Press:  12 March 2014

Z. Balogh  and
G. Gruenhage
Z. Balogh
Affiliation:
Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056
G. Gruenhage
Affiliation:
Division of Mathematics, Auburn University, Auburn, Alabama 36849
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Abstract

It is shown that Con(ZF) implies Con(ZFC + there exists a Dowker filter on ω2). The problem is also considered on higher cardinals.

Keywords

Dowker filterλ-Dowker filterforcing iteration with < κ-supports
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 4 , December 1991 , pp. 1284 - 1289
Copyright
Copyright © Association for Symbolic Logic 1991

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References

REFERENCES

[D]Dowker, C. H., A problem in set theory, Journal of the London Mathematical Society, vol. 27 (1952), pp. 371–374.CrossRefGoogle Scholar
[FP]Freiling, C. and Payne, T. H., Some properties of large filters, this Journal, vol. 53 (1988), pp. 1027–1035.Google Scholar
[K]Kunen, K., Set theory, North-Holland, Amsterdam, 1980.Google Scholar
[R]Rudin, M. E., Two problems of Dowker, Proceedings of the American Mathematical Society, vol. 91 (1984), pp. 155–158.CrossRefGoogle Scholar