2014/08/01 by Gregory Mckay, Gregory McKay, McKay, Gregory
Computer Science · Mathematics · #05C05 (Secondary) #06A06 #06A07 (Primary) 03E05 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras #math.LO #msc:03E05 #msc:05C05 #msc:06A06 #msc:06A07
paper · pdf · doi:10.48550/arxiv.1408.0315
v1: 45 pages, 8 figures; v2: 44 pages, 11 figures, minor corrections, fixed typos, new figures and some notational changes to improve clarity; v3: 45 pages, 12 figures, changed the way the paper is structured to improve clarity and provide examples earlier on
openalex publication_date 2014/08/01 · arxiv created 2014/10/01 · arxiv updated 2014/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a method of constructing better-quasi-orders by generalising a technique for constructing operator algebras that was developed by Pouzet. We then generalise the notion of σ-scattered to partial orders, and use our method to prove that the class of σ-scattered partial orders is better-quasi-ordered under embeddability. This generalises theorems of Laver, Corominas and Thomassé regarding σ-scattered linear orders and trees, countable forests and N-free partial orders respectively. In particular, a class of countable partial orders is better-quasi-ordered whenever the class of indecomposable subsets of its members satisfies a natural strengthening of better-quasi-order.