# FINITARY REDUCIBILITY ON EQUIVALENCE RELATIONS

@article{Miller2016FINITARYRO,
title={FINITARY REDUCIBILITY ON EQUIVALENCE RELATIONS},
author={R. Miller and K. M. Ng},
journal={The Journal of Symbolic Logic},
year={2016},
volume={81},
pages={1225 - 1254}
}
• Published 2016
• Computer Science, Mathematics
• The Journal of Symbolic Logic
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… Expand
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#### References

SHOWING 1-10 OF 33 REFERENCES
COMPLEXITY OF EQUIVALENCE RELATIONS AND PREORDERS FROM COMPUTABILITY THEORY
• Computer Science, Mathematics
• The Journal of Symbolic Logic
• 2014
• 16
• PDF
On Σ11 equivalence relations over the natural numbers
• Mathematics, Computer Science
• Math. Log. Q.
• 2012
• 18
• PDF
The effective theory of Borel equivalence relations
• Mathematics, Computer Science
• Ann. Pure Appl. Log.
• 2010
• 22
• PDF
UNIVERSAL COMPUTABLY ENUMERABLE EQUIVALENCE RELATIONS
• Mathematics, Computer Science
• The Journal of Symbolic Logic
• 2014
• 39
• PDF
Equivalence Relations on Classes of Computable Structures
• Mathematics, Computer Science
• CiE
• 2009
• 21
• PDF
Classifications of Computable Structures
• Computer Science, Mathematics
• Notre Dame J. Formal Log.
• 2018
• 4
• PDF
Classification from a Computable Viewpoint
• Computer Science, Mathematics
• Bulletin of Symbolic Logic
• 2006
• 24
• PDF