05999306

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05999306 Tandareanu, Nicolae Zamfir, Cristina Slices and extensions of $\omega$-trees. An. Univ. Craiova, Ser. Mat. Inf. 38, No. 1, 72-82 (2011). 2011 University of Craiova, Faculty of Mathematics \& Computer Science, Craiova EN directed ordered graph tree ordered tree partial order embedding mapping Zbl 1212.05036 Zbl 1224.05233 Summary: We defined the structure named $\omega$-labeled tree as a binary, ordered and labeled tree with several features concerning the labels and order between the direct descendants of a node [{\it N. \c T\u and\u areanu} and {\it C. Zamfir}, An. Univ. Craiova, Ser. Mat. Inf. 37, No.\,1, 80--89 (2010; Zbl 1212.05036)]. In this paper we introduce two operators, which enable us to compare between them the structures or parts thereof. These operators work in opposite directions: one of them obtains some part of the structure and the other operator extends the structure. Both the first and the second operator preserves the basic features of an $\omega$-tree from the point of view of the comparison binary relations and the equivalence relations introduced in [loc. cit.] and [{\it N. \c T\u and\u areanu} and {\it C. Zamfir}, An. Univ. Craiova, Ser. Mat. Inf. 37, No.\,2, 7--17 (2010; Zbl 1224.05233)].