A Dedekind Finite Borel Set
Logic
2008-06-13 v1
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.
Cite
@article{arxiv.0806.1957,
title = {A Dedekind Finite Borel Set},
author = {Arnold W. Miller},
journal= {arXiv preprint arXiv:0806.1957},
year = {2008}
}
Comments
Latex2e: 21 pages Latest version at http://www.math.wisc.edu/~miller