Asimetrični pravilni tipovi

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Asimetrični pravilni tipovi

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dc.contributor.advisor Tanović, Predrag
dc.contributor.author Moconja, Slavko
dc.date.accessioned 2016-08-30T08:15:57Z
dc.date.available 2016-08-30T08:15:57Z
dc.date.issued 2015
dc.identifier.uri http://hdl.handle.net/123456789/4282
dc.description.abstract In this thesis we study asymmetric regular types. If p is regular and asymmetric over A, then there exists an order such that Morley sequences in p over A are strictly increasing. It turns out that for every small model M A, the order type of a maximal Morley sequence in p over A whose elements are from M does not depend on the choice of the sequence, i.e. it is an invariant of the model M denoted by Invp;A(M). In the countable case we can determine all possibilities for Invp;A(M): either Invp;A(M) is an arbitrary countable linear order or, provided that it contains at least two elements, it is a countable dense linear order (possibly with one or both endpoints). Also, we study the connection between Invp;A(M) and Invq;A(M), where p and q are two regular and asymmetric over A types such that p A 6?w q A. We distinguish two kinds of non-orthogonality: bounded and unbounded. Under the assumption that p and q are convex, in the bounded case we get that Invp;A(M) and Invq;A(M) are either isomorphic or anti-isomorphic, while under the assumption of strong regularity, in the unbounded case we get that Dedekind completions of Invp;A(M) and Invq;A(M) are either isomorphic or anti-isomorphic. In particular we study the following class of structures: expansions of linear orderings with countably many unary predicates and countably many equivalence relations with convex classes. We provide new examples of regular types. Namely, it turns out that every global invariant type in this context is regular, and every non-algebraic type over A has precisely two global extensions which are invariant over A. We also study the connection between the question of existence of a quasi- minimal model of a complete rst-order theory and the question of existence of a global strongly regular type. We also deal with the problem whether every quasi- minimal group must be abelian. It turns out that this question has the positive answer provided that the global extension of the generic type of a quasi-minimal group is asymmetric over ;. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2016-08-30T08:15:57Z No. of bitstreams: 1 phdMoconja_Slavko.pdf: 2254694 bytes, checksum: 8a3c2e21862739b9beb80d852e0bfa28 (MD5) en
dc.description.provenance Made available in DSpace on 2016-08-30T08:15:57Z (GMT). No. of bitstreams: 1 phdMoconja_Slavko.pdf: 2254694 bytes, checksum: 8a3c2e21862739b9beb80d852e0bfa28 (MD5) Previous issue date: 2015 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title Asimetrični pravilni tipovi en_US
mf.author.birth-date 1984-10-11
mf.author.birth-place Sremska Mitrovica 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 global type, invariant type, regular type, Morley sequence, invariant, quasi-minimal structure, linear ordering, algebraic closure operator en_US
mf.subject.subarea Mathematical logic en_US
mf.contributor.committee Božić, Milan
mf.contributor.committee Ikodinović, Nebojša
mf.contributor.committee Krupinski, Krzysztof
mf.contributor.committee Petrović, Zoran
mf.contributor.committee Tanović, Predrag
mf.university.faculty Mathematical Faculty en_US
mf.document.references 20 en_US
mf.document.pages 110 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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