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

Takayuki Kihara

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arXiv · 1803.03753

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

Takayuki Kihara

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Abstract

In this article, we study an analogue of $tt$-reducibility for points in computable metric spaces. We characterize the notion of the metric $tt$-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.

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BibTeX RIS

Takayuki Kihara. 2018-03-10. On a metric generalization of the $tt$-degrees and effective dimension theory. https://arxiv.org/abs/1803.03753

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