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arXiv · 0806.1957

A Dedekind Finite Borel Set

Arnold W. Miller
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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.

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BibTeXRIS

Arnold W. Miller. 2008-06-11. A Dedekind Finite Borel Set. https://arxiv.org/abs/0806.1957

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