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 u ≤ f is either comparable with both e and d, or incomparable with both.
Citation
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
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