Some structural properties of quasi-degrees
Roland Sh. Omanadze · Logic Journal of IGPL · 2017
We study the structural properties of |$Q$|-degrees and prove that every non-computable c.e. |$Q$|-degree contains a perfect set. Using this result and Batyrshin’s theorem [4] we have that there is a non-computable c.e. |$Q$|-degree containing a single c.e. |$1$|-degree. We show that if |$K$| is a creative set, then there is a |$\Sigma^0_2\setminus\Delta^0_2$| set |$B$| which is |$Q$|-incomparable with |$K$| and for all c.e. sets |$W$|, if |$W\leq_{Q} B$| then |$W\leq_{Q}\varnothing$|.