A Dedekind Finite Borel Set
| dc.creator | Miller, Arnold W. | |
| dc.date | 2008-06-11 | |
| dc.date.accessioned | 2026-07-07T09:44:08Z | |
| dc.date.available | 2026-07-07T09:44:08Z | |
| dc.description | 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. | |
| dc.description | Latex2e: 21 pages Latest version at http://www.math.wisc.edu/~miller | |
| dc.identifier | https://arxiv.org/abs/0806.1957 | |
| dc.identifier | http://arxiv.org/abs/0806.1957 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162762 | |
| dc.subject | Logic | |
| dc.subject | 03E25, 03E15 | |
| dc.title | A Dedekind Finite Borel Set | |
| dc.type | text |