Title: A Dedekind Finite Borel Set
Author: Arnold W. Miller
Abstract: In this paper we prove three theorems about the
theory of Borel sets in models of ZF without any form of
the axiom of choice. We prove that if B is a G-delta-sigma
set, then either B is countable or B contains a perfect
subset. Second, we prove that if the real line is the
countable union of countable sets, then there exists an
F-sigma-delta set which is uncountable but contains no
perfect subset. Finally, we construct a model of ZF in
which we have an infinite Dedekind finite set of reals
which is F-sigma-delta.
Latex2e: 21 pages
Latest version at: www.math.wisc.edu/~miller