English

On a metric generalization of the $tt$-degrees and effective dimension theory

Logic 2018-03-13 v1 Logic in Computer Science

Abstract

In this article, we study an analogue of tttt-reducibility for points in computable metric spaces. We characterize the notion of the metric tttt-degree in the context of first-level Borel isomorphism. Then, we study this concept from the perspectives of effective topological dimension theory and of effective fractal dimension theory.

Keywords

Cite

@article{arxiv.1803.03753,
  title  = {On a metric generalization of the $tt$-degrees and effective dimension theory},
  author = {Takayuki Kihara},
  journal= {arXiv preprint arXiv:1803.03753},
  year   = {2018}
}