Please use this identifier to cite or link to this item:
https://open.uns.ac.rs/handle/123456789/29030
Title: | Partial orders of isomorphic substructures of relational structures Parcijalna uredjenja izomorfnih podstruktura relacijskih stuktura |
Authors: | Kuzeljević Boriša | Keywords: | linear order, partial order, relational structure, isomorphic copy;linearno uredjenje, relacijska struktura, izomorfna kopija, parcijalno uredjenje | Issue Date: | 2-Jun-2014 | Publisher: | Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu University of Novi Sad, Faculty of Sciences at Novi Sad |
Abstract: | <p>Cilj ove teze je da se ispitaju lanci u parcijalnim uredjenjima (P(X), ⊂), pri čemu je P(X) skup domena izomorfnih podstruktura relacijske strukture X. Pošto 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 podstrukture, onda je svaki maksimalan lanac u (P(X) ∪ {∅} , ⊂) kompletno linearno uredjenje koje se utapa u R i ima neizolovan minimum. Ako je X relacijska struktura, dat je dovoljan uslov da za svako kompletno linearno uredjenje L koje se utapa u R i ima neizolovan minimum, postoji maksimalan lanac u (P(X) ∪ {∅} , ⊂) izomorfan L. Dokazano je i da ako je X neka od sledećih relacijskih struktura: Rado graf, Hensonov graf, random poset, ultrahomogeni poset Bn ili ultrahomogeni poset Cn; onda je L izomorfno maksimalnom lancu u (P(X) ∪ {∅} , ⊂) ako i samo ako je L kompletno, utapa se u R i ima neizolovan minimum. Ako je X prebrojiv antilanac ili disjunktna unija µ kompletnih grafova sa ν tačaka za µν = ω, onda je L izomorfno maksimalnom lancu u (P(X) ∪ {∅} , ⊂) ako i samo ako je bulovsko, utapa se u R i ima neizolovan minimum.</p> <p>The purpose of this thesis is to investigate chains in partial orders (P(X), ⊂), where P(X) is the set of domains of isomorphic substructures of a relational structure X. Since each chain in a partial 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 chain in (P(X)∪ {∅} , ⊂) is a complete, R-embeddable linear order with minimum non-isolated. If X is a relational structure, a condition is given for X, which is sufficient for (P(X) ∪ {∅} , ⊂) to embed each complete, R-embeddable linear order with minimum non-isolated as a maximal chain. 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 chain in (P(X) ∪ {∅} , ⊂) if and only if L is complete, R-embeddable with minimum non-isolated. If X is a countable antichain or disjoint union of µ complete graphs with ν points where µν = ω, then L is isomorphic to a maximal chain in (P(X) ∪ {∅} , ⊂) if and only if L is Boolean, R-embeddable with minimum non-isolated.</p> |
URI: | https://open.uns.ac.rs/handle/123456789/29030 |
Appears in Collections: | PMF Teze/Theses |
Show full item record
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.