Skip to main content Accessibility help

A high strongly noncappable degree

  • Steffen Lempp (a1)


An r.e. degree a0, 0′ is called strongly noncappable if it has no inf with any incomparable r.e. degree. We show the existence of a high strongly noncappable degree.



Hide All
[AS84] Ambos-Spies, K., On pairs of recursively enumerable degrees, Transactions of the American Mathematical Society, vol. 283 (1984), pp. 507531.
[Cota] Cooper, S. B., A jump class of noncappable degrees, this Journal (to appear).
[La66] Lachlan, A. H., Lower bounds for pairs of recursively enumerable degrees, Proceedings of the London Mathematical Society, ser. 3, vol. 16 (1966), pp. 537569.
[Sa63] Sacks, G. E., On the degrees less than 0′, Annals of Mathematics, ser. 2, vol. 77 (1963), pp. 211231.
[Sa64] Sacks, G. E., The recursively enumerable degrees are dense, Annals of Mathematics, ser. 2, vol. 80 (1964), pp. 300312.
[Sh65] Shoenfield, J. R., Application of model theory to degrees of unsolvability, Symposium on the theory of models (Addison, J. al, editors), North-Holland, Amsterdam, 1965, pp. 359363.
[Shta] Shore, R. A., A noninversion theorem for the jump operator, Annals of Pure and Applied Logic (to appear).
[So80] Soare, R. I., Fundamental methods for constructing recursively enumerable degrees, Recursion theory: its generalizations and applications (proceedings of Logic Colloquium ’79; F. Drake, R. and Wainer, S. S., editors), London Mathematical Society Lecture Note Series, vol. 45, Cambridge University Press, Cambridge, 1980, pp. 151.
[So85] Soare, R. I., Tree arguments in recursion theory and the 0″ -priority method in recursion theory, Recursion theory (Nerode, A. and Shore, R. A., editors), Proceedings of Symposia in Pure Mathematics, vol. 42, American Mathematical Society, Providence, Rhode Island, 1985, pp. 53106.
[So87] Soare, R. I., Recursively enumerable sets and degrees, Springer-Verlag, Berlin, 1987.
[Ya66] Yates, C. E. M., A minimal pair of recursively enumerable degrees, this Journal, vol. 31 (1966), pp. 159168.


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