"Rich families and elementary submodels"@en . "7" . . "RIV/00216208:11320/14:10210855" . "PL - Polsk\u00E1 republika" . . . "http://dx.doi.org/10.2478/s11533-013-0400-z" . . "Rich families and elementary submodels" . . . "42711" . "We compare two methods of proving separable reduction theorems in functional analysis - the method of rich families and the method of elementary submodels. We show that any result proved using rich families holds also when formulated with elementary submodels and the converse is true in spaces with fundamental minimal system and in spaces of density aleph_1. We do not know whether the converse is true in general. We apply our results to show that a projectional skeleton may be without loss of generality indexed by ranges of its projections." . . . . "C\u00FAth, Marek" . "Rich family; Projectional skeleton; Separable reduction; Elementary submodel"@en . "We compare two methods of proving separable reduction theorems in functional analysis - the method of rich families and the method of elementary submodels. We show that any result proved using rich families holds also when formulated with elementary submodels and the converse is true in spaces with fundamental minimal system and in spaces of density aleph_1. We do not know whether the converse is true in general. We apply our results to show that a projectional skeleton may be without loss of generality indexed by ranges of its projections."@en . . "[72224E335BE7]" . "Rich families and elementary submodels" . "I, P(GAP201/12/0290), S" . . "14"^^ . . . . "1895-1074" . "12" . "10.2478/s11533-013-0400-z" . "2"^^ . . . "Central European Journal of Mathematics" . "11320" . "RIV/00216208:11320/14:10210855!RIV15-MSM-11320___" . . . . "2"^^ . "Rich families and elementary submodels"@en . "000334180800008" . "Kalenda, Ond\u0159ej" .