Half of an inseparable pair
| dc.creator | Miller, Arnold W. | |
| dc.date | 2004-07-23 | |
| dc.date.accessioned | 2026-07-07T05:10:38Z | |
| dc.date.available | 2026-07-07T05:10:38Z | |
| dc.description | A classical theorem of Luzin is that the separation principle holds for the Pi^0_alpha sets but fails for the Sigma^0_alpha sets. We show that for every Sigma^0_alpha set A which is not Pi^0_alpha there exists a Sigma^0_alpha set B which is disjoint from A but cannot be separated from A by a Delta^0_alpha set C. Assuming Pi^1_1-determancy it follows from a theorem of Steel that a similar result holds for Pi^1_1 sets. On the other hand assuming V=L there is a proper Pi^1_1 set which is not half of a Borel inseparable pair. These results answer questions raised by F.Dashiell. Latest version at: www.math.wisc.edu/~miller/ | |
| dc.description | LaTex2e 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0407405 | |
| dc.identifier | http://arxiv.org/abs/math/0407405 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71985 | |
| dc.subject | Logic | |
| dc.subject | 03E15, 03E35, 03E60 | |
| dc.title | Half of an inseparable pair | |
| dc.type | text |