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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

Citations:

Zbl 0799.03047
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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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