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Mapping a set of reals onto the reals

Published online by Cambridge University Press:  12 March 2014

Arnold W. Miller
Arnold W. Miller*
Affiliation:
University of Texas, Austin, Texas 78712
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Abstract

In this paper we show that it is consistent with ZFC that for any set of reals of cardinality the continuum, there is a continuous map from that set onto the closed unit interval. In fact, this holds in the iterated perfect set model. We also show that in this model every set of reals which is always of first category has cardinality less than or equal to ω1.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 3 , September 1983 , pp. 575 - 584
Copyright
Copyright © Association for Symbolic Logic 1983

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References

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