The gamma - Borel conjecture

dc.creatorMiller, Arnold W.
dc.date2003-12-16
dc.date.accessioned2026-07-07T05:03:57Z
dc.date.available2026-07-07T05:03:57Z
dc.descriptionIn 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.descriptionLaTex2e, 16 pages
dc.identifierhttps://arxiv.org/abs/math/0312308
dc.identifierhttp://arxiv.org/abs/math/0312308
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69619
dc.subjectLogic
dc.subject03E35
dc.titleThe gamma - Borel conjecture
dc.typetext

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