Vol. 76, No. 1, 1978

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Realizing partial orderings by classes of co-simple sets

Jeffrey Brian Remmel

Vol. 76 (1978), No. 1, 169–184
Abstract

We show that we can embed any countable partial ordering into a class of co-r.e. bi-dense subsets of the rationals, each subset of a fixed nonzero r.e. Turing degree, under an order induced by recursive similarity transformations. Also, we show that we can embed any countable partial ordering into the co-simple isols under either the order induced by addition of isols or the order induced by recursive injections.

Mathematical Subject Classification
Primary: 02F40, 02F40
Secondary: 06A10, 02F25
Milestones
Received: 2 February 1977
Revised: 19 August 1977
Published: 1 May 1978
Authors
Jeffrey Brian Remmel