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1 results

  • On Downey's conjecture

  • Marat M. Arslanov, Iskander Sh. Kalimullin, Steffen Lempp
  • Journal:
    The Journal of Symbolic Logic / Volume 75 / Issue 2 / June 2010
    Published online by Cambridge University Press:
    12 March 2014, pp. 401-441
    Print publication:
    June 2010

  • 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.