Countable 1-transitive coloured linear orderings II

G. Campero-Arena ¹   ; J. K. Truss ²

¹ Departamento de Matemáticas Facultad de Ciencias Universidad Nacional Autónoma de México Ciudad Universitaria M{é}xico, D.F. 04510, Mexico
² Department of Pure Mathematics University of Leeds Leeds LS2 9JT, England

Fundamenta Mathematicae, Tome 183 (2004) no. 3, pp. 185-213

Résumé

This paper gives a structure theorem for the class of countable $1$-transitive coloured linear orderings for a countably infinite colour set, concluding the work begun in [1]. There we gave a complete classification of these orders for finite colour sets, of which there are $\aleph _1$. For infinite colour sets, the details are considerably more complicated, but many features from [1] occur here too, in more marked form, principally the use (now essential it seems) of coding trees, as a means of describing the structures in our list, of which there are now $2^{\aleph _0}$.

Détail

DOI : 10.4064/fm183-3-1

Keywords: paper gives structure theorem class countable transitive coloured linear orderings countably infinite colour set concluding work begun there gave complete classification these orders finite colour sets which there aleph infinite colour sets details considerably complicated many features occur here too marked form principally essential seems coding trees means describing structures list which there aleph