Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Incompleteness theorems for random reals
Advances in Applied Mathematics
An easy priority-free proof of a theorem of Friedberg
Theoretical Computer Science
Theoretical Computer Science
Visualization 2001 Conference (Acm
Visualization 2001 Conference (Acm
The arithmetical complexity of dimension and randomness
ACM Transactions on Computational Logic (TOCL)
An Introduction to Kolmogorov Complexity and Its Applications
An Introduction to Kolmogorov Complexity and Its Applications
Computability and Randomness
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
How powerful are integer-valued martingales?
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Kolmogorov complexity and the recursion theorem
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
| Hi-index | 0.00 |
We investigate enumerability properties for classes of sets which permit recursive, lexicographically increasing approximations, or left-r.e. sets. In addition to pinpointing the complexity of left-r.e. Martin-Löf, computably, Schnorr, and Kurtz random sets, weakly 1-generics and their complementary classes, we find that there exist characterizations of the third and fourth levels of the arithmetic hierarchy purely in terms of these notions. More generally, there exists an equivalence between arithmetic complexity and existence of numberings for classes of left-r.e. sets with shift-persistent elements. While some classes (such as Martin-Löf randoms and Kurtz nonrandoms) have left-r.e. numberings, there is no canonical, or acceptable, left-r.e. numbering for any class of left-r.e. randoms. Finally, we note some fundamental differences between left-r.e. numberings for sets and reals.