Uniform Enumeration Operations
Lachlan, A. H.
J. Symbolic Logic, Tome 40 (1975) no. 1, p. 401-409 / Harvested from Project Euclid
Sacks [2] has asked whether there exists a uniform solution to Post's problem, i.e. an enumeration operation $W$ such that $\mathbf{d} < W(\mathbf{d}) < \mathbf{d}'$ for every degree $\mathbf{d}$. 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: $\mathbf{d} < W(\mathbf{d})$ for all $\mathbf{d}$. In addition, it is proved that the only other uniform enumeration operations such that $\mathbf{d} \leq W (\mathbf{d})$ for all $\mathbf{d}$ are those which equal the identity operation above some fixed degrees.
Publié le : 1975-09-14
Classification: 
@article{1183739472,
     author = {Lachlan, A. H.},
     title = {Uniform Enumeration Operations},
     journal = {J. Symbolic Logic},
     volume = {40},
     number = {1},
     year = {1975},
     pages = { 401-409},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183739472}
}
Lachlan, A. H. Uniform Enumeration Operations. J. Symbolic Logic, Tome 40 (1975) no. 1, pp.  401-409. http://gdmltest.u-ga.fr/item/1183739472/