RUS  ENG
Full version
JOURNALS // Algebra i logika

Algebra Logika, 2003, Volume 42, Number 1, Pages 3–25 (Mi al14)

Splitting Properties of Total Enumeration Degrees
M. M. Arslanov, I. Sh. Kalimullin, S. B. Cooper

References

1. C. G. Jockusch, Jr., “Semirecursive sets and positive reducibility”, Trans. Am. Math. Soc., 131:2 (1968), 420–436  crossref  mathscinet  zmath
2. S. Ahmad, “Embedding the diamond in the $\Sigma_2$ enumeration degrees”, J. Symb. Log., 56:1 (1991), 195–212  crossref  mathscinet  zmath
3. S. Ahmad, A. H. Lachlan, “Some special pairs of $\Sigma_2$ $e$-degrees”, Math. Log. Q., 44:4 (1998), 431–449  crossref  mathscinet  zmath
4. M. M. Arslanov, S. B. Cooper, I. Sh. Kalimullin, A. Li, Total degrees and non-splitting properties of $\Sigma^0_2$-enumeration degrees (to appear)
5. S. B. Cooper, C. S. Copestake, “Properly $\Sigma_2$ enumeration degrees”, Z. Math. Logik Grundlagen Math., 34:6 (1988), 491–522  crossref  mathscinet  zmath
6. S. B. Cooper, “Enumeration reducibility, nondeterministic computations and relative computability of partial functions”, Recursion Theory Week, Lect. Notes Math., 1432, eds. K. Ambos-Spies, G. Müller, G. E. Sacks, 1990, 57–110  mathscinet  zmath
7. A. Sorbi, “The enumeration degrees of the $\Sigma^0_2$ sets”, Complexity, Logic and Recursion Theory, 1997, ed. A. Sorbi, Marcel Dekker, New York, 303–330  mathscinet  zmath
8. P. G. Odifreddi, Classical Recursion Theory, v. II, Studies Logic Found. Math., 143, North-Holland, Amsterdam, 1999  mathscinet
9. A. Sorbi, “Sets of generator and automorphism bases for the enumeration degrees”, Ann. Pure Appl. Log., 94:1–3 (1998), 263–272  crossref  mathscinet  zmath
10. M. M. Arslanov, A. Sorbi, “Relative splittings of $0'_e$ in the $\Delta_2^0$-enumeration degrees”, Logic Colloquium 98, Lect. Notes Log., 13, eds. Buss S. Pudlak P., Springer-Verlag, Berlin a. o., 2000, 44–56  mathscinet
11. R. I. Soare, Recursively Enumerable Sets and Degrees, Perspect. Math. Log., Omega Series, Springer-Verlag, Heidelberg a. o., 1987  mathscinet; R. I. Soar, Vychislimo perechislimye mnozhestva i stepeni, Kazanskoe matem. ob-vo, Kazan, 2000  mathscinet  zmath
12. A. Nies, A. Sorbi, Branching in the enumeration degrees of the $\Sigma_2^0$ sets (to appear)
13. S. B. Cooper, L. Harrington, A. H. Lachlan, S. Lempp, R. I. Soare, “The $d$-r.e. degrees are not dense”, Ann. Pure Appl. Logic, 55:2 (1991), 125–151  crossref  mathscinet  zmath


© Steklov Math. Inst. of RAS, 2025