Journal of Symbolic Logic

On Downey's conjecture

Marat M. Arslanov, Iskander Sh. Kalimullin, and Steffen Lempp

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

J. Symbolic Logic Volume 75, Issue 2 (2010), 401-441.

First available in Project Euclid: 18 March 2010

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03D28: Other Turing degree structures

d.c.e. degrees n-c.e. degrees Downey's conjecture


Arslanov, Marat M.; Kalimullin, Iskander Sh.; Lempp, Steffen. On Downey's conjecture. J. Symbolic Logic 75 (2010), no. 2, 401--441. doi:10.2178/jsl/1268917488.

Export citation