Annals of Pure and Applied Logic 118 (1-2):61-85 (2002)

Abstract
We investigate the orbit of a low computably enumerable set under automorphisms of the partial order of c.e. sets under inclusion. Given an arbitrary low c.e. set A and an arbitrary noncomputable c.e. set C, we use the New Extension Theorem of Soare to construct an automorphism of mapping A to a set B such that CTB. Thus, the orbit in of the low set A cannot be contained in the upper cone above C. This complements a result of Harrington, who showed that the orbit of a noncomputable c.e. set cannot be contained in the lower cone below any incomplete c.e. set
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DOI 10.1016/s0168-0072(01)00119-1
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Jumps of Hemimaximal Sets.Rod Downey & Mike Stob - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (8):113-120.
Jumps of Hemimaximal Sets.Rod Downey & Mike Stob - 1991 - Mathematical Logic Quarterly 37 (8):113-120.

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