Analiza prebrojivih modela potpunih teorija linearno uređenih struktura

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Analiza prebrojivih modela potpunih teorija linearno uređenih struktura

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dc.contributor.advisor Tanović, Predrag
dc.contributor.author Ilić, Dejan
dc.date.accessioned 2017-04-19T15:02:46Z
dc.date.available 2017-04-19T15:02:46Z
dc.date.issued 2016
dc.identifier.uri http://hdl.handle.net/123456789/4452
dc.description.abstract We study linearly ordered structures and their complete theories. The main technical tools used in the analysis are condensations, i.e. partitioning the ordering into convex parts and then studying the quotient structure and that of the parts. We introduce a uniformly definable condensation relation cδ that decomposes the ordering into largest convex pieces whose first order theory is simple: they are either dense or discrete orderings. We study cδ quotient structures that are expansions of certain simple countable discrete orderings and give a precise description of those having Cantor Bendixson rank 1. We also use the condensation cδ to prove that any linear ordering expanded by finitely many unary predicates and equivalence relations with convex classes is interpretable in a pure linear ordering. We introduce notions of linear and strong linear binarity for linearly ordered structures and their complete theories. In the case of a theory, the defining condition expresses a property of the automorphism group of its saturated model. We prove that any complete theory of a linear ordering with unary predicates and equivalence relations with convex classes is strongly linearly binary. The main result states that a strongly linearly binary structure is definitionally equivalent to a linear ordering with unary predicates and equivalence relation with convex classes added. In the proof we give a description of definable sets in any linear ordering with unary predicates and equivalence relations with convex classes. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2017-04-19T15:02:46Z No. of bitstreams: 1 disertacija_IlicDejan.pdf: 756759 bytes, checksum: acf74bf4b3436f31643d4aa9749abd38 (MD5) en
dc.description.provenance Made available in DSpace on 2017-04-19T15:02:46Z (GMT). No. of bitstreams: 1 disertacija_IlicDejan.pdf: 756759 bytes, checksum: acf74bf4b3436f31643d4aa9749abd38 (MD5) Previous issue date: 2016 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title Analiza prebrojivih modela potpunih teorija linearno uređenih struktura en_US
mf.author.birth-date 2016
mf.author.birth-place Beograd en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srbin en_US
mf.subject.area Mathematics en_US
mf.subject.keywords Linear orderings, expansions of linear orderings, definable condensations, simple type, binary theories, linear binarity, strong linear binarity, convex equivalences, definitional equivalence, quantifier elimination en_US
mf.subject.subarea Mathematical logic en_US
mf.contributor.committee Ikodinović, Nebojša
mf.contributor.committee Kurulić, Miloš
mf.contributor.committee Petrović, Aleksandar
mf.contributor.committee Petrović, Zoran
mf.contributor.committee Tanović, Predrag
mf.university.faculty Mathematical Faculty en_US
mf.document.references 21 en_US
mf.document.pages 86 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

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