Long Borel Hierarchies
| dc.creator | Miller, Arnold W. | |
| dc.date | 2007-04-30 | |
| dc.date.accessioned | 2026-07-07T07:58:50Z | |
| dc.date.available | 2026-07-07T07:58:50Z | |
| dc.description | We show that it is relatively consistent with ZF that the Borel hierarchy on the reals has length $ω_2$. This implies that $ω_1$ has countable cofinality, so the axiom of choice fails very badly in our model. A similar argument produces models of ZF in which the Borel hierarchy has length any given limit ordinal less than $ω_2$, e.g., $ω$ or $ω_1+ω_1$. Latex2e: 24 pages plus 8 page appendix Latest version at: www.math.wisc.edu/~miller | |
| dc.identifier | https://arxiv.org/abs/0704.3998 | |
| dc.identifier | http://arxiv.org/abs/0704.3998 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128148 | |
| dc.subject | Logic | |
| dc.subject | 03E15;03E25;03E35 | |
| dc.title | Long Borel Hierarchies | |
| dc.type | text |