This is an announcement for the paper "Rich families and elementary submodels" by Marek Cuth and Ondrej F.K. Kalenda.
Abstract: 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 an 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.
Archive classification: math.FA
Mathematics Subject Classification: 46B26, 03C30
Submitted from: cuthm5am@karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.1818
or