The Journal of Symbolic Logic

Research Article

Mapping a set of reals onto the reals

Arnold W. Miller 1

University of Texas, Austin, Texas 78712


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 ω 1.

(Received May 28 1981)


1  Research partially supported by an NSF grant