## Journal of Symbolic Logic

### Mapping a Set of Reals Onto the Reals

Arnold W. Miller

#### 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 $\omega_1$.

#### Article information

Source
J. Symbolic Logic, Volume 48, Issue 3 (1983), 575-584.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183741316

Mathematical Reviews number (MathSciNet)
MR716618

Zentralblatt MATH identifier
0527.03031

JSTOR