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Parcijalna uredjenja izomorfnih podstruktura relacijskih stuktura

Partial orders of isomorphic substructures of relational structures

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Disertacija.pdf (928.5Kb)
IzvestajKomisije.pdf (212.6Kb)
Author
Kuzeljević, Boriša
Mentor
Kurilić, Miloš
Committee members
Pilipović, Stevan
Kurilić, Miloš
Grulović, Milan
Mijajlović, Žarko
Šobot, Boris
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Abstract
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 minimu...m. 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.

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 wit...h 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.

Faculty:
Универзитет у Новом Саду, Природно-математички факултет
Date:
02-06-2014
Projects:
  • Set Theory, Model Theory and Set-Theoretic Topology (RS-174006)
Keywords:
linearno uredjenje / linear order / relacijska struktura / izomorfna kopija / parcijalno uredjenje / partial order / relational structure / isomorphic copy
[ Google Scholar ]
Handle
https://hdl.handle.net/21.15107/rcub_nardus_1747
URI
http://www.cris.uns.ac.rs/DownloadFileServlet/Disertacija139513071805425.pdf?controlNumber=(BISIS)85727&fileName=139513071805425.pdf&id=1582&source=NaRDuS&language=sr
https://nardus.mpn.gov.rs/handle/123456789/1747
http://www.cris.uns.ac.rs/record.jsf?recordId=85727&source=NaRDuS&language=sr
http://www.cris.uns.ac.rs/DownloadFileServlet/IzvestajKomisije13951307253253.pdf?controlNumber=(BISIS)85727&fileName=13951307253253.pdf&id=1583&source=NaRDuS&language=sr

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