## Density of the lattice of $$m$$th degrees of conditional problems.(English. Russian original)Zbl 0873.03041

Sib. Math. J. 37, No. 6, 1110-1112 (1996); translation from Sib. Mat. Zh. 37, No. 6, 1266-1268 (1996).
A paper by 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.

### MSC:

 03D30 Other degrees and reducibilities in computability and recursion theory

### Keywords:

conditional problem; density; lattice of $$m$$-degrees

Zbl 0799.03047
Full Text:

### References:

 [1] Gao Su, ”The degrees of conditional problems,” J. Symbol. Logic,59, No. 1, 166–181 (1994). · Zbl 0799.03047 [2] Yu. L. Ershov.”On index sets,” Sibirsk. Mat. Zh.,11, No. 2, 326–342 (1970).
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