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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Parcijalna uredjenja izomorfnih podstruktura relacijskih stuktura / Partial orders of isomorphic substructures of relational structures

Kuzeljević Boriša 02 June 2014 (has links)
<p>Cilj ove teze je da se ispitaju&nbsp; lanci u parcijalnim uredjenjima (P(X), &sub;),&nbsp;pri čemu je P(X) skup domena izomorfnih podstruktura relacijske strukture&nbsp;X. Po&scaron;to se svaki lanac u parcijalnom uredjenju može produžiti do maksimalnog lanca, dovoljno je ispitati maksimalne lance u P(X). Dokazano je da, ako je X ultrahomogena relacijska struktura koja ima netrivijalne izomorfne&nbsp;podstrukture, onda je svaki maksimalan lanac u (P(X) &cup; {&empty;}&nbsp; , &sub;) kompletno&nbsp;linearno uredjenje koje se utapa u R i ima neizolovan minimum. Ako &nbsp;je X&nbsp;relacijska struktura, dat je dovoljan uslov da za svako kompletno linearno uredjenje L koje se utapa&nbsp; u R i ima neizolovan minimum, postoji maksimalan lanac u (P(X) &cup; {&empty;}&nbsp; , &sub;) izomorfan L.&nbsp; Dokazano je i da ako je&nbsp;X neka od sledećih relacijskih struktura: Rado graf, Hensonov graf, random poset, ultrahomogeni&nbsp; poset Bn&nbsp; ili&nbsp; ultrahomogeni&nbsp; poset Cn; onda je&nbsp;L izomorfno maksimalnom lancu u (P(X) &cup; {&empty;}&nbsp; , &sub;) ako i samo ako je &nbsp;L&nbsp;kompletno,&nbsp; utapa se u R i ima neizolovan minimum. Ako je X prebrojiv&nbsp;antilanac ili disjunktna unija &micro; kompletnih&nbsp; grafova sa &nu; tačaka za &micro;&nu; = &omega;, onda je L izomorfno maksimalnom lancu u (P(X) &cup; {&empty;}&nbsp; , &sub;) ako i samo ako&nbsp;je bulovsko,&nbsp; utapa se u R i ima neizolovan minimum.</p> / <p>The purpose of this thesis is to investigate chains in partial orders (P(X), &sub;), where P(X) is the set of domains of isomorphic substructures of a relational structure X. Since each chain in a partial&nbsp; order can be extended to a maximal one, it is enough to describe maximal chains in P(X). It is proved that, if X is an ultrahomogeneous relational structure with non-trivial isomorphic substructures, then each maximal&nbsp; chain in (P(X)&cup; {&empty;}&nbsp; , &sub;) is a complete, R-embeddable linear order with minimum&nbsp; non-isolated. If X is a relational structure, a condition is given for X, which is sufficient&nbsp; for (P(X) &cup; {&empty;}&nbsp; , &sub;) to embed each complete,&nbsp; R-embeddable&nbsp; linear order with minimum non-isolated as a maximal&nbsp; chain.&nbsp; It is also proved that if X is one of the follow- ing relational structures: Rado graph, Henson graph, random poset, ultrahomogeneous poset Bn or ultrahomogeneous poset Cn; then L is isomorphic to a maximal&nbsp; chain in (P(X) &cup; {&empty;}&nbsp; , &sub;) if and only if L is complete, R-embeddable with minimum non-isolated. If X is a countable&nbsp; antichain&nbsp; or disjoint union of &micro; complete graphs with &nu; points where &micro;&nu; = &omega;, then L is isomorphic to a maximal&nbsp; chain&nbsp; in (P(X) &cup; {&empty;}&nbsp; , &sub;) if and only if L is Boolean, R-embeddable with minimum non-isolated.</p>

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