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### On Downey's conjecture

Marat M. Arslanov, Iskander Sh. Kalimullin, and Steffen Lempp
Source: J. Symbolic Logic Volume 75, Issue 2 (2010), 401-441.

#### 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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Primary Subjects: 03D28
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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1268917488
Digital Object Identifier: doi:10.2178/jsl/1268917488
Zentralblatt MATH identifier: 05725857
Mathematical Reviews number (MathSciNet): MR2648149

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