Quasi-o-minimal structures

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dc.contributor.authorBelegradek, O
dc.contributor.authorPeterzil, Y
dc.contributor.authorWagner, F
dc.date.accessioned2024-07-18T20:49:16Z
dc.date.available2024-07-18T20:49:16Z
dc.date.issued2000
dc.departmentİstanbul Bilgi Üniversitesien_US
dc.description.abstractA structure (M, <....) is called quasi-o-minimal if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal: one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use ii to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any quasi-o-minimal ordered ring is a real closed field, or has zero multiplication; every quasi-o-minimal divisible ordered group is o-minimal; every quasi-o-minimal archimedian densely ordered group is divisible. We show that a counterpart of quasi-o-minimality in stability theory is the notion of theory of U-rank 1.en_US
dc.identifier.doi10.2307/2586690
dc.identifier.endpage1132en_US
dc.identifier.issn0022-4812
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-0034259280en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage1115en_US
dc.identifier.urihttps://doi.org/10.2307/2586690
dc.identifier.urihttps://hdl.handle.net/11411/8127
dc.identifier.volume65en_US
dc.identifier.wosWOS:000089597400007en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherAssn Symbolic Logic Incen_US
dc.relation.ispartofJournal of Symbolic Logicen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectQuasi-O-Minimal Theoryen_US
dc.subjectO-Minimal Theoryen_US
dc.subjectOrdered Groupen_US
dc.subjectTheory Of U-Rank 1en_US
dc.titleQuasi-o-minimal structuresen_US
dc.typeArticleen_US

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