Browsing Mathematical Sciences by Author "Kuzeljević, Boriša"
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Kuzeljević, Boriša (Novi Sad , 2013)[more][less]
Abstract: The purpose of this thesis is to investigate chains in partial orders (P(X), C), where 11} (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) U {0} , C) 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) U {0} , C) 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 following relational structures: Rado graph, Henson graph, random poset, ultrahomogeneous poset 1,13, or ultrahomogeneous poset C, 2 ; then L is isomorphic to a maximal chain in (P(X) U {0} , C) if and only if L is complete, R-embeddable with minimum non-isolated. If X is a countable antichain or disjoint union of u complete graphs on v vertices with pv = then L is isomorphic to a maximal chain in 0P(X) U {0} , c) if and only if L is Boolean, R-embeddable with minimum non-isolated. URI: http://hdl.handle.net/123456789/3873 Files in this item: 1
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