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dc.contributor.authorFarah, Ilijasen
dc.contributor.authorSolecki, Sławomiren
dc.date.accessioned2020-04-27T10:33:40Z-
dc.date.available2020-04-27T10:33:40Z-
dc.date.issued2006-01-30en
dc.identifier.issn0001-8708en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/790-
dc.description.abstractWe study three classes of subgroups of Polish groups: Borel subgroups, Polishable subgroups, and maximal divisible subgroups. The membership of a subgroup in each of these classes allows one to assign to it a rank, that is, a countable ordinal, measuring in a natural way complexity of the subgroup. We prove theorems comparing these three ranks and construct subgroups with prescribed ranks. In particular, answering a question of Mauldin, we establish the existence of Borel subgroups which are Πα0-complete, α≥3, and Σα0-complete, α≥2, in each uncountable Polish group. Also, for every α<ω1 we construct an Abelian, locally compact, second countable group which is densely divisible and of Ulm length α + 1. All previously known such groups had Ulm length 0 or 1.en
dc.publisherElsevier-
dc.relationNational Science Foundation (USA), Grants DMS-40313-00 01, DMS-9803676 and DMS-0102254-
dc.relation.ispartofAdvances in Mathematicsen
dc.subjectBorel complexity of subgroups | Densely divisible groups | Maximal divisible subgroups | Polish groups | Polishable subgroupsen
dc.titleBorel subgroups of Polish groupsen
dc.typeArticleen
dc.identifier.doi10.1016/j.aim.2005.07.009en
dc.identifier.scopus2-s2.0-28944447244en
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage499en
dc.relation.lastpage541en
dc.relation.issue2en
dc.relation.volume199en
dc.description.rankM21a-
item.openairetypeArticle-
item.fulltextNo Fulltext-
item.grantfulltextnone-
item.cerifentitytypePublications-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
crisitem.author.orcid0000-0001-7703-6931-
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