Concerning partial recursive similarity transformations of linearly ordered sets
Louise Hay, Alfred B. Manaster, Joseph G. Rosenstein · Pacific Journal of Mathematics · 1977
Interesting contrasts between uncountable suborderings of the continuum and denumerable linear orderings are provided by results of Dushnik and Miller and Sierpiήski on the one hand and Laver on other.We investigate analogues of these results in a recursive setting where the only similarity maps are restrictions of partial recursive functions.Complements of recursively enumerable bi-dense subsets of the rationale of arbitrary nonzero degree of unsolvability are shown to bear a strong resemblance to uncountable suborderings of the continuum.