Random strings and tt-degrees of Turing complete C.E. sets

@article{Cai2014RandomSA,
  title={Random strings and tt-degrees of Turing complete C.E. sets},
  author={Mingzhong Cai and Rodney G. Downey and Rachel Epstein and Steffen Lempp and Joseph S. Miller},
  journal={Log. Methods Comput. Sci.},
  year={2014},
  volume={10}
}
We investigate the truth-table degrees of (co-)c.e.\ sets, in particular, sets of random strings. It is known that the set of random strings with respect to any universal prefix-free machine is Turing complete, but that truth-table completeness depends on the choice of universal machine. We show that for such sets of random strings, any finite set of their truth-table degrees do not meet to the degree~0, even within the c.e. truth-table degrees, but when taking the meet over all such truth… 
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