Slices and extensions of ω-trees

Abstract

In \cite{ntcz1} we defined the structure named ω-labeled tree as a binary, ordered and labeled tree with several features concerning the labels and order between the direct descendants of a node. 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 ω-tree from the point of view of the comparison binary relations and the equivalence relations introduced in \cite{ntcz1} and \cite{ntcz2}.