We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
FINITARY REDUCIBILITY ON EQUIVALENCE RELATIONS.
- Authors
MILLER, RUSSELL; NG, KENG MENG
- Abstract
We introduce the notion of finitary computable reducibility on equivalence relations on the domain ω. This is a weakening of the usual notion of computable reducibility, and we show it to be distinct in several ways. In particular, whereas no equivalence relation can be ${\rm{\Pi }}_{n + 2}^0$-complete under computable reducibility, we show that, for every n, there does exist a natural equivalence relation which is ${\rm{\Pi }}_{n + 2}^0$-complete under finitary reducibility. We also show that our hierarchy of finitary reducibilities does not collapse, and illustrate how it sharpens certain known results. Along the way, we present several new results which use computable reducibility to establish the complexity of various naturally defined equivalence relations in the arithmetical hierarchy.
- Subjects
COMPUTABLE functions; COMPUTABILITY logic; EQUIVALENCE relations (Set theory); RECURSION theory; MATHEMATICAL readiness
- Publication
Journal of Symbolic Logic, 2016, Vol 81, Issue 4, p1225
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2016.23