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

Harold T. Hodes

Vol. 108 (1983), No. 1, 115–119

DOI: 10.2140/pjm.1983.108.115

Abstract

Given a sequence of Turing degrees ⟨a_i⟩_i<ω,a_i < a_i+1, is there a function of f such that (i) deg(f) is a minimal upper bound on ⟨a_i⟩_i<ω, and (ii) {deg((f)_n)∣n < ω} = {a_i∣i < ω}? In this note we show that the most natural minimal upper bound on ⟨a_i⟩_i<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