Journal of Symbolic Logic

On Downey's conjecture

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

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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

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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.

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