Splitting theorems and low degrees

Issue title: Oberwolfach Workshop on Computability Theory 2018

Guest editors: Vasco Brattka, Rod Downey, Julia F. Knight and Steffen Lempp

Article type: Research Article

Authors: Chih, Ellen^a | Downey, Rod G.^{b; *}

Affiliations: [a] Mathematics Department, University of California, Berkeley, CA 94720, USA | [b] School of Mathematics and Statistics, Victoria University, P.O. Box 600, Wellington, New Zealand. rod.downey@vuw.ac.nz

Correspondence: [*] Corresponding author. rod.downey@vuw.ac.nz.

Abstract: We prove that if A is a non-low c.e. set, then there exists noncomputable sets A1⊔A2=A splitting A with A1 non-low.

Keywords: Splitting, low, computably enumerable set, non-uniformity, domination

DOI: 10.3233/COM-180093

Journal: Computability, vol. 8, no. 3-4, pp. 243-252, 2019