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

Keywords

Primary 03D30Secondary 03C6203D7854H05truth table degreeeffective dimensioncomputable metic space
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 2 , June 2019 , pp. 726 - 749
Copyright
Copyright © The Association for Symbolic Logic 2019 

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