Abstract
What are the possible cardinalities of subsets of the reals? R itself has power 2א0; it is trivial to exhibit subsets of the integers of any power ≦א0. The Continuum Hypothesis of Cantor conjectures that these examples exhaust the possible cardinalities of subsets of R .
The main results of this paper (Theorem 1 through 3) were obtained independently a few months later by R. Mansfield.
The author is a Sloan Foundation fellow. This research was partially supported by National Science Foundation grant GP-5632.
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Solovay, R.M. (1969). On the Cardinality of \( \sum_2^1 \) Sets of Reals. In: Bulloff, J.J., Holyoke, T.C., Hahn, S.W. (eds) Foundations of Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-86745-3_7
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