Structural theory of trees II. Completeness and completions of trees
DOI:
https://doi.org/10.55016/ojs/cdm.v18i2.74005Abstract
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.
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Copyright (c) 2023 Ruaan Kellerman, Alberto Zanardo, Valentin Goranko
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