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Some points in βN

Published online by Cambridge University Press:  24 October 2008

Kenneth Kunen
Kenneth Kunen
Affiliation:
University of Wisconsin
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Abstract

Assuming either the continuum hypothesis or Martin's axiom, we show that in the space βN – N, there are: (a) points which are not P-points, but which are also not limit points of any countable set, and (b) a countable set of points dense in itself such that each of the points is not a limit point of any countable discrete set. Our method is to construct such points in the Stone space of a measure algebra, and then embed that Stone space into βN – N. We also, by a similar use of measures, establish the independence of the existence of selective ultrafilters by showing that there are none in the random real model.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 3 , November 1976 , pp. 385 - 398
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

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