Structural theory of trees II. Completeness and completions of trees

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Ruaan Kellerman, Alberto Zanardo, Valentin Goranko

Published: 2023, Last Modified: 14 Oct 2024Contributions Discret. Math. 2023EveryoneRevisionsBibTeXCC BY-SA 4.0
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 tree completions that extend any tree to a minimal one satisfying the respective completeness property.