# Rich families and elementary submodels

Open Mathematics (2014)

- Volume: 12, Issue: 7, page 1026-1039
- ISSN: 2391-5455

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topMarek Cúth, and Ondřej Kalenda. "Rich families and elementary submodels." Open Mathematics 12.7 (2014): 1026-1039. <http://eudml.org/doc/268948>.

@article{MarekCúth2014,

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 and in spaces of density ℵ1. 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.},

author = {Marek Cúth, Ondřej Kalenda},

journal = {Open Mathematics},

keywords = {Elementary submodel; Separable reduction; Projectional skeleton; Rich family; elementary submodel; separable reduction; projectional skeleton; rich family},

language = {eng},

number = {7},

pages = {1026-1039},

title = {Rich families and elementary submodels},

url = {http://eudml.org/doc/268948},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Marek Cúth

AU - Ondřej Kalenda

TI - Rich families and elementary submodels

JO - Open Mathematics

PY - 2014

VL - 12

IS - 7

SP - 1026

EP - 1039

AB - 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 ℵ1. 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.

LA - eng

KW - Elementary submodel; Separable reduction; Projectional skeleton; Rich family; elementary submodel; separable reduction; projectional skeleton; rich family

UR - http://eudml.org/doc/268948

ER -

## References

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