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ON A METRIC GENERALIZATION OF THE tt-DEGREES AND EFFECTIVE DIMENSION THEORY

Published online by Cambridge University Press:  12 March 2019

TAKAYUKI KIHARA*
Affiliation:
GRADUATE SCHOOL OF INFORMATICS NAGOYA UNIVERSITY, NAGOYA 464-8601, JAPANE-mail: kihara@i.nagoya-u.ac.jp

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.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2019 

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ON A METRIC GENERALIZATION OF THE tt-DEGREES AND EFFECTIVE DIMENSION THEORY
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