The gamma - Borel conjecture
| dc.creator | Miller, Arnold W. | |
| dc.date | 2003-12-16 | |
| dc.date.accessioned | 2026-07-07T05:03:57Z | |
| dc.date.available | 2026-07-07T05:03:57Z | |
| dc.description | In this paper we show that it is relatively consistent with ZFC that every gamma-set is countable while not every strong measure zero set is countable. This answers a question of Paul Szeptycki. A set is a gamma-set iff every omega-cover contains a gamma-subcover. An open cover is an omega-cover iff every finite set is covered by some element of the cover. An open cover is a gamma-cover iff every element of the space is in all but finitely many elements of the cover. Gerlits and Nagy proved that every gamma-set has strong measure zero. We also show that is consistent that every strong gamma-set is countable while there exists an uncountable gamma-set. On the other hand every strong measure zero set is countable iff every set with the Rothberger property is countable. | |
| dc.description | LaTex2e, 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0312308 | |
| dc.identifier | http://arxiv.org/abs/math/0312308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69619 | |
| dc.subject | Logic | |
| dc.subject | 03E35 | |
| dc.title | The gamma - Borel conjecture | |
| dc.type | text |