@article {IOPORT.05999306, author = {Tandareanu, Nicolae and Zamfir, Cristina}, title = {Slices and extensions of $\omega$-trees.}, year = {2011}, journal = {Analele Universit\u a\c tii din Craiova. Seria Matematic\u a Informatic\u a}, volume = {38}, number = {1}, issn = {1223-6934}, pages = {72-82}, publisher = {University of Craiova, Faculty of Mathematics \& Computer Science, Craiova}, abstract = {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)].}, identifier = {05999306}, }