Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees

Rodney G. Downey · Keng Meng Ng · Reed Solomon

ກ.ຍ. 2020 · Memoirs of the American Mathematical Society ຫົວທີ 265 · American Mathematical Soc.

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First, there are sets with minimal weak truth table degree which bound noncomputable computably enumerable sets under Turing reducibility. Second, no set with computable enumerable Turing degree can have minimal weak truth table degree. Third, no $Delta^0_2$ set which Turing bounds a promptly simple set can have minimal weak truth table degree.