Uniform enumeration operations
- 1 September 1975
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 40 (3) , 401-409
- https://doi.org/10.2307/2272164
Abstract
Sacks [2] has asked whether there exists a uniform solution to Post's problem, i.e. an enumeration operation W such that d < W(d) < d′ for every degree d. It is shown here that if such an operation W exists it cannot itself in a particular technical sense be uniform. In fact, the jump operation is characterized amongst such uniform enumeration operations by the condition: d < W(d) for all d. In addition, it is proved that the only other uniform enumeration operations such that d ≤ W(d) for all d are those which equal the identity operation above some fixed degree.Keywords
This publication has 1 reference indexed in Scilit:
- On a theorem of Lachlan and MartinProceedings of the American Mathematical Society, 1967