THE n-r.e. DEGREES: UNDECIDABILITY AND Σ1 SUBSTRUCTURES
Mingzhong Cai, Richard A. Shore, Theodore A. Slaman · Journal of Mathematical Logic · 2012
We study the global properties of [Formula: see text], the Turing degrees of the n-r.e. sets. In Theorem 1.5, we show that the first order of [Formula: see text] is not decidable. In Theorem 1.6, we show that for any two n and m with n < m, [Formula: see text] is not a Σ1-substructure of [Formula: see text].