Defining the Turing jump

Mathematical Research Letters

Volumn 6, Issue 5-6, 1999, Pages 711-722

  Shore, Richard A ^a   Slaman, Theodore A ^b  

^a Cornell University ^*  (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033235855     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/mrl.1999.v6.n6.a10     Document Type: Article

References (13)

1. [1] S.B. Cooper, The jump is definable in the structure of the degrees of unsolvability, Bull. Amer. Math. Soc. 23 (1990), 151-158.
2. [2] E. Griffor (ed.), Handbook of computability theory, North-Holland Publishing Co., Amsterdam, 1999.
3. [3] G.G. Jockusch, Jr. and R.A. Shore, Pseudo-jump operators II: Transfinite iterations, hierarchies, and minimal covers, J. Symbolic Logic 49 (1984), 1205-1236.
4. [4] C.G. Jockusch, Jr. and R.I. Soare, Minimal covers and arithmetical sets, Proc. Amer. Math. Soc. 25 (1970), 856-859.
5. 1 classes and degrees of theories, Trans. Amer. Math. Soc. 173 (1972), 33-56.
6. [6] S.C. Kleene and E.L. Post, The upper semi-lattice of degrees of recursive unsolvability, Ann. of Math. 59 (1954), 379-407.
7. [7] A.H. Lachlan, A recursively enumerable degree which will not split over all lesser ones, Ann. Math. Logic 9 (1975), 307-365.
8. [8] G.E. Sacks, On the degrees less than 0′, Ann. of Math. (1963), 211-231.
9. [9] R.A. Shore, The structure of the degrees of unsolvability, in Recursion theory (Ithaca, N.Y., 1982), pp. 33-51, Amer. Math. Soc., Providence, R.I., 1985.
10. [10] R.A. Shore and T.A. Slaman, A splitting theorem for n-REA degrees, unpublished.
11. [11] T. A. Slaman, Degree structures, in Proceedings of the International Congress of Mathematicians, Vol. I (Kyoto, 1990), pp. 303-316, Springer-Verlag, Heidelberg, 1991.
12. [12] T.A. Slaman and W.H. Woodin, Definability in degree structures, unpublished.
13. [13] A.M. Turing, Systems of logic based on ordinals, Proc. London Math. Soc. (3) 45 (1939), 161-228.