DC FieldValueLanguage
dc.contributor.authorBrech, Christinaen
dc.contributor.authorLopez-Abad, Jorgeen
dc.contributor.authorTodorčević, Stevoen
dc.date.accessioned2020-05-01T20:29:21Z-
dc.date.available2020-05-01T20:29:21Z-
dc.date.issued2018-08-20en
dc.identifier.issn0001-8708en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/2171-
dc.description.abstractWe study density requirements on a given Banach space that guarantee the existence of subsymmetric basic sequences by extending Tsirelson's well-known space to larger index sets. We prove that for every cardinal κ smaller than the first Mahlo cardinal there is a reflexive Banach space of density κ without subsymmetric basic sequences. As for Tsirelson's space, our construction is based on the existence of a rich collection of homogeneous families on large index sets for which one can estimate the complexity on any given infinite set. This is used to describe detailedly the asymptotic structure of the spaces. The collections of families are of independent interest and their existence is proved inductively. The fundamental stepping up argument is the analysis of such collections of families on trees.en
dc.publisherElsevier-
dc.relationFAPESP, Grants 2012/24463-7, 2015/26654-2 and 2013/24827-1-
dc.relationCNPq, Grants 307942/2012-0 and 454112/2015-7-
dc.relationMinisterio de Economía y Competitividad, Grant MTM2012-31286-
dc.relationUSP-COFECUB, Grant 31466UC-
dc.relationNSERC, Grant 455916-
dc.relationCNRS, Grant UMR7586-
dc.relation.ispartofAdvances in Mathematicsen
dc.subjectFamilies of finite sets | Nonseparable Banach spaces | Spreading modelsen
dc.titleHomogeneous families on trees and subsymmetric basic sequencesen
dc.typeArticleen
dc.identifier.doi10.1016/j.aim.2018.06.008en
dc.identifier.scopus2-s2.0-85049340784en
dc.relation.firstpage322en
dc.relation.lastpage388en
dc.relation.volume334en
dc.description.rankM21a-
item.cerifentitytypePublications-
item.fulltextNo Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.openairetypeArticle-
item.grantfulltextnone-
crisitem.author.orcid0000-0003-4543-7962-
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