RUS  ENG
Полная версия
ЖУРНАЛЫ // Ученые записки Казанского университета. Серия Физико-математические науки

Учен. зап. Казан. ун-та. Сер. Физ.-матем. науки, 2012, том 154, книга 2, страницы 204–217 (Mi uzku1132)

Isolation: motivations and applications
G. Wu, M. M. Yamaleev

Литература

1. Cooper S. B., Yi X., Isolated d. r. e. degrees, Preprint series, № 17, University of Leeds, Dept. of Pure Math., 1995, 25 pp.
2. LaForte G., “Isolation in the $CEA$ hierarchy”, Arch. Math. Logic, 44:2 (2005), 227–244  crossref  mathscinet  zmath  isi  elib
3. Arslanov M., Kalimullin I., Lempp S., “On Downey's conjecture”, J. Symbolic Logic, 75:2 (2010), 401–441  crossref  mathscinet  zmath  isi  elib
4. Cai M., Shore R. A., Slaman T. A., “The $n$-r. e. degrees: undecidability and $\Sigma_1$ substructures”, J. Math. Logic, 12:1 (2012), 1250005-1–1250005-30  crossref  mathscinet  zmath  isi  elib
5. Wu G., Structural Properties of d. c. e. degrees and presentations of c. e. reals, Ph D Thesis, Victoria University of Wellington, Wellington, 2002
6. Fang C., Liu J., Wu G., “Cupping and diamond embeddings: a unifying approach”, Lecture Notes in Computer Science, 6735, 2011, 71–80  crossref  mathscinet  zmath
7. Soare R. I., Recursively enumerable sets and degrees, Springer-Verlag, Heidelberg, 1987, 437 pp.  mathscinet
8. Cooper S. B., “Local degree theory”, Handbook of Computability Theory, Studies in Logic and the Foundations of Mathematics, 140, ed. E. R. Griffor, North-Holland, Amsterdam, 1999, 121–153  crossref  mathscinet
9. Arslanov M., “Open questions about the $n$-c. e. degrees”, Computability Theory and Its Applications: Current Trends and Open Problems, Proc. 1999 AMS-IMS-SIAM Joint Summer Res. Conf., Contemporary Mathematics, 257, eds. M. Lerman, P. A. Cholak, S. Lempp, R. A. Shore, Amer. Math. Soc., Providence, RI, 2000, 15–22  crossref  mathscinet  zmath
10. Cooper S. B., Degrees of Unsolvability, Ph D Thesis, University of Leicester, Leicester, 1971
11. Cooper S. B., Harrington L., Lachlan A. H., Lempp S., Soare R. I., “The d. r. e. degrees are not dense”, Ann. Pure Appl. Logic, 55:2 (1991), 125–151  crossref  mathscinet  zmath  isi
12. Arslanov M., “Structural properties of the degrees below $0'$”, Dokl. Acad. Nauk SSSR, 283:2 (1985), 270–273  mathnet  mathscinet  zmath  isi
13. Downey R., “D. r. e. degrees and the nondiamond theorem”, Bull. London Math. Soc., 21 (1989), 43–50  crossref  mathscinet  zmath  isi
14. Ishmukhametov Sh., D. r. e. sets, their degrees and index sets, Ph D Thesis, Novosibirsk, 1986
15. Kaddah D., “Infima in the d. r. e. degrees”, Ann. Pure Appl. Logic, 62 (1993), 207–263  crossref  mathscinet  zmath  isi
16. Ding D., Qian L., “Isolated d. r. e. degrees are dense in r. e. degree structure”, Arch. Math. Logic, 36:1 (1996), 1–10  crossref  mathscinet  zmath  adsnasa  isi
17. LaForte G., “The isolated d. r. e. degrees are dense in the r. e. degrees”, Math. Logic Quart., 42 (1996), 83–103  crossref  mathscinet  zmath  isi
18. Arslanov M. M., Lempp S., Shore R. A., “On isolating r. e. and isolated d-r. e. degrees”, Computability, enumerability, unsolvability, London Mathematical Society, Lecture Note Series, 224, eds. S. B. Cooper, T. A. Slaman, S. S. Wainer, Cambridge Univ. Press, Cambridge, 1996, 61–80  mathscinet  zmath
19. Ishmukhametov Sh., Wu G., “Isolation and the high/low hierarchy”, Arch. Math. Logic, 41:3 (2002), 259–266  crossref  mathscinet  zmath  isi
20. Li A., Wu G., Yang Y., “Bounding computably enumerable degrees in the Ershov hierarchy”, Ann. Pure Appl. Logic, 141:1–2 (2006), 79–88  mathscinet  zmath  isi  elib
21. Cooper S. B., “Minimal pairs and high recursively enumerable degrees”, J. Symbolic Logic, 39:4 (1974), 655–660  crossref  mathscinet
22. Chong C. T., Li A., Yang Y., “The existence of high nonbounding degrees in the difference hierarchy”, Ann. Pure Appl. Logic, 138:1–3 (2006), 31–51  crossref  mathscinet  zmath  isi  elib
23. Cooper S. B., Salts M. C., Wu G., “The non-isolating degrees are upwards dense in the computably enumerable degrees”, Theory and Applications of Models of Computation, Proc. 5th Int. Conf. TAMC 2008, Lecture Notes in Computer Science, 4978, Springer-Verlag, Berlin–Heidelberg, 2008, 588–596  crossref  mathscinet  zmath
24. Salts M., “An interval of computably enumerable isolating degrees”, Math. Logic Quart., 45 (1999), 59–72  crossref  mathscinet  zmath  isi
25. Lachlan A. H., “Lower bounds for pairs of recursively enumerable degrees”, Proc. London Math. Soc., 16 (1966), 537–569  crossref  mathscinet  zmath
26. Yang Y., Yu L., “On $\Sigma_1$-structural differences among finite levels of the Ershov hierarchy”, J. Symbolic Logic, 71:4 (2006), 1223–1236  crossref  mathscinet  zmath  isi
27. Wu G., “On the density of the pseudo-isolated degrees”, Proc. London Math. Soc., 88:2 (2004), 273–288  crossref  mathscinet  zmath  isi
28. Ishmukhametov Sh., “On the r. e. predecessors of d. r. e. degrees”, Arch. Math. Logic, 38:6 (1999), 373–386  crossref  mathscinet  zmath  isi
29. Wu G., “Isolation and lattice embeddings”, J. Symbolic Logic, 67:3 (2002), 1055–1064  crossref  mathscinet  zmath  isi
30. Liu J., Wu G., “An almost-universal cupping degree”, J. Symbolic Logic, 76:4 (2011), 1137–1152  crossref  mathscinet  zmath  isi
31. Cooper S. B., Li A., “Splitting and cone avoidance in the d. c. e. degrees”, Sci. China Ser. A, 45:9 (2002), 1135–1146  mathscinet  zmath
32. Yamaleev M. M., “Splitting in 2-computably enumerable degrees with avoiding cones”, Russian Mathematics (Izv. Vuz. Mat.), 53:6 (2009), 63–66  mathnet  crossref  mathscinet  zmath
33. Arslanov M., LaForte G., Slaman T., “Relative enumerability in the difference hierarchy”, J. Symbolic Logic, 63:2 (1998), 411–420  crossref  mathscinet  zmath  isi
34. Li A., Song Y., Wu G., “Universal cupping degrees”, Theory and Applications of Models of Computation, Proc. 3rd Int. Conf. TAMC 2006, Lecture Notes in Computer Science, 3959, Springer-Verlag, Berlin–Heidelberg, 2006, 721–730  crossref  mathscinet  zmath
35. Downey R. G., Li A., Wu G., “Complementing cappable degrees in the difference hierarchy”, Ann. Pure Appl. Logic, 125:1–3 (2004), 101–118  crossref  mathscinet  zmath  isi


© МИАН, 2026