On better quasi-ordering countable trees
type: Item
instance of: scholarly article
title: On better quasi-ordering countable trees
zbMATH Open document ID: 0575.05024
DOI: 10.1016/0012-365X(85)90127-X
author: E. Corominas
published in: Discrete Mathematics
publication date: 1985-01-01T00:00:00Z
review text: In order to obtain a better-quasi-order of the class of countable trees, the author studies ordinal algebras and in particular ordinal algebras associated with trees. Basically, if a (universal) algebra is equipped with a quasi-order such that the operators are increasing and extensive and such that the values increase with the operators, then the resulting algebra is an ordinal algebra. The author derives results for ordinal algebras and for those associated with trees to demonstrate that the class of countable trees is better-quasi-ordered under embeddability. Besides deriving a considerable collection of results, the author is also able to provide a good setting for certain other results, e.g., Pouzet's basis theorem or to make use of results such as the Ramsey-Nash-Williams theorem. In the journey from chains to more complex ordered structures, this paper should prove a valuable addition.
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 06F25
zbMATH DE Number: 3918389
zbMATH Keywords: canonical
zbMATH Keywords: indecomposable
zbMATH Keywords: embedding
zbMATH Keywords: ordinal isomorphism preserving infimums
zbMATH Keywords: countable trees
zbMATH Keywords: ordinal algebras
reviewed by: J. Neggers
MaRDI profile type: Publication
cites work: Q5650887
cites work: Ordering by Divisibility in Abstract Algebras
cites work: Well-Quasi-Ordering, The Tree Theorem, and Vazsonyi's Conjecture
cites work: On Fraissé's order type conjecture
cites work: An order type decomposition theorem
cites work: Q3890740
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description: scientific article; zbMATH DE number 3918389