Skip to main content Accessibility help
×
Home

NON-SPLITTINGS OF SPEEDABLE SETS

  • ELLEN S. CHIH (a1)

Abstract

We construct a speedable set that cannot be split into speedable sets. This solves a question of Bäuerle and Remmel.

Copyright

References

Hide All
[1]Bäuerle, Frank A. and Remmel, Jeffrey B., On speedable and levelable vector spaces. Annals of Pure and Applied Logic, vol. 67 (1994), no. 13, pp. 61112. A selection of papers presented at the symposium “Logic at Tver ’92” (Tver', 1992).
[2]Bennison, Victor L. and Soare, Robert I., Some lowness properties and computational complexity sequences. Theoretical Computer Science, vol. 6 (1978), no. 3, pp. 233254.
[3]Blum, M. and Marques, I., On complexity properties of recursively enumerable sets, this Journal, vol. 38 (1973), pp. 579–593.
[4]Blum, Manuel, A machine-independent theory of the complexity of recursive functions. Journal of the Association for Computing Machinery, vol. 14 (1967), pp. 322336.
[5]Barry Cooper, S. and Goncharov, Sergey S. (editors), Computability and models, The University Series in Mathematics, Kluwer Academic/Plenum Publishers, New York, 2003.
[6]Downey, Rod and Stob, Michael, Splitting theorems in recursion theory. Annals of Pure and Applied Logic, vol. 65 (1993), no. 1, p. 106.
[7]Friedberg, Richard M., Three theorems on recursive enumeration. I. Decomposition. II. Maximal set. III. Enumeration without duplication, this Journal, vol. 23 (1958), pp. 309–316.
[8]Jahn, Michael A., Implicit measurements of dynamic complexity properties and splittings of speedable sets, this Journal, vol. 64 (1999), no. 3, pp. 1037–1064.
[9]Lachlan, Alistair H., A recursively enumerable degree which will not split over all lesser ones. Annals of Mathematical Logic, vol. 9 (1976), no. 4, pp. 307365.
[10]Maass, Wolfgang, Characterization of recursively enumerable sets with supersets effectively isomorphic to all recursively enumerable sets. Transactions of the American Mathematical Society, vol. 279 (1983), no. 1, pp. 311336.
[11]Omanadze, Roland Sh., Splittings of effectively speedable sets and effectively levelable sets, this Journal, vol. 69 (2004), no. 1, pp. 143–158.
[12]Sacks, Gerald E., On the degrees less than 0'. Annals of Mathematics (2), vol. 77 (1963), pp. 211231.
[13]Soare, Robert I., Computational complexity, speedable and levelable sets, this Journal, vol. 42 (1977), no. 4, pp. 545–563.
[14]Soare, Robert I., Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1987.

Keywords

NON-SPLITTINGS OF SPEEDABLE SETS

  • ELLEN S. CHIH (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed