Vol. 108, No. 1, 1983

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A minimal upper bound on a sequence of Turing degrees which represents that sequence

Harold T. Hodes

Vol. 108 (1983), No. 1, 115–119
Abstract

Given a sequence of Turing degrees aii<ω,ai < ai+1, is there a function of f such that (i) deg(f) is a minimal upper bound on aii<ω, and (ii) {deg((f)n)n < ω} = {aii < ω}? In this note we show that the most natural minimal upper bound on aii<ω is of the form deg(f) for such an f.

Mathematical Subject Classification 2000
Primary: 03D30
Milestones
Received: 3 November 1981
Revised: 23 July 1982
Published: 1 September 1983
Authors
Harold T. Hodes