Vol. 71, No. 1, 1977

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Concerning partial recursive similarity transformations of linearly ordered sets

Louise Hay, Alfred Berry Manaster and Joseph Goeffrey Rosenstein

Vol. 71 (1977), No. 1, 57–70

Interesting contrasts between uncountable suborderings of the continuum and denumerable linear orderings are provided by results of Dushnik and Miller and Sierpiński 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 rationals of arbitrary nonzero degree of unsolvability are shown to bear a strong resemblance to uncountable suborderings of the continuum.

Mathematical Subject Classification 2000
Primary: 02F25, 02F25
Secondary: 06A05
Received: 8 June 1976
Published: 1 July 1977
Louise Hay
Alfred Berry Manaster
Joseph Goeffrey Rosenstein