Density of the lattice of \(m\)th degrees of conditional problems (Q1357968)

A paper by \textit{Su Gao} [J. Symb. Log. 59, 166-181 (1994; Zbl 0799.03047)] treated different notions of reducibility, including \(m\)-reducibility, for so-called conditional problems, represented by ordered pairs of sets of natural numbers. The present paper gives a simple Kleene-Post argument, alleged to prove the density of the lattice of \(m\)-degrees (rendered ``\(m\)th degrees'' in this translation) of conditional problems. However, the result is false in the form stated in the paper; there are errors in the handling of the distinction between what Gao called trivial and nontrivial degrees.