Structural theory of trees. II. Completeness and completions of trees
Combinatorics
2023-01-18 v1 Logic
Abstract
Trees are partial orderings where every element has a linearly ordered set of smaller elements. We define and study several natural notions of completeness of trees, extending Dedekind completeness of linear orders and Dedekind-MacNeille completions of partial orders. We then define constructions of \emph{tree completions} that extend any tree to a minimal one satisfying the respective completeness property.
Keywords
Cite
@article{arxiv.2301.06352,
title = {Structural theory of trees. II. Completeness and completions of trees},
author = {Valentin Goranko and Ruaan Kellerman and Alberto Zanardo},
journal= {arXiv preprint arXiv:2301.06352},
year = {2023}
}
Comments
22 pages. To appear in: Contributions to Discrete Mathematics