A Dedekind Finite Borel Set

Details A Dedekind Finite Borel Set A Dedekind Finite Borel Set

2008-06-11

arxiv.org/abs/0806.1957v1

Mathematics

Logic

Latex2e: 21 pages Latest version at http://www.math.wisc.edu/~miller

Scientific paper

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.

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