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}
}
  • R. Miller, K. M. Ng
  • 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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