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

2023/01/16 by Goranko, Valentin, Kellerman, Ruaan, Zanardo, Alberto
#05C05 #06A06 #06B23 #Combinatorics (math.CO) #FOS: Mathematics #G.2.0 #Logic (math.LO)

paper · doi:10.48550/arxiv.2301.06352

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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