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June 2010 On Downey's conjecture
Marat M. Arslanov, Iskander Sh. Kalimullin, Steffen Lempp
J. Symbolic Logic 75(2): 401-441 (June 2010). DOI: 10.2178/jsl/1268917488

Abstract

We prove that the degree structures of the d.c.e. and the 3-c.e. Turing degrees are not elementarily equivalent, thus refuting a conjecture of Downey. More specifically, we show that the following statement fails in the former but holds in the latter structure: There are degrees f > e > d > 0 such that any degree uf is either comparable with both e and d, or incomparable with both.

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Marat M. Arslanov. Iskander Sh. Kalimullin. Steffen Lempp. "On Downey's conjecture." J. Symbolic Logic 75 (2) 401 - 441, June 2010. https://doi.org/10.2178/jsl/1268917488

Information

Published: June 2010
First available in Project Euclid: 18 March 2010

zbMATH: 1192.03017
MathSciNet: MR2648149
Digital Object Identifier: 10.2178/jsl/1268917488

Subjects:
Primary: 03D28

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 2 • June 2010
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