Structural theory of trees. II. Completeness and completions of trees

Kellerman, Ruaan; Zanardo, Alberto; Goranko, Valentin

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Structural theory of trees. II. Completeness and completions of trees

Kellerman, Ruaan; Zanardo, Alberto; Goranko, Valentin

URI: http://hdl.handle.net/2263/97233

Date: 2023-12

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.

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