Rich families and elementary submodels

Marek Cúth; Ondřej Kalenda

Open Mathematics (2014)

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

Abstract

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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.

How to cite

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Marek 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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