Realizing partial orderings by classes of co-simple sets

Jeffrey Brian Remmel

Vol. 76 (1978), No. 1, 169–184

DOI: 10.2140/pjm.1978.76.169

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