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THE SIMPLEST LOW LINEAR ORDER WITH NO COMPUTABLE COPIES

Part of: Computability and recursion theory Model theory

Published online by Cambridge University Press:  10 June 2022

ANDREY FROLOV Open the ORCID record for ANDREY FROLOV [Opens in a new window]  and
MAXIM ZUBKOV Open the ORCID record for MAXIM ZUBKOV [Opens in a new window]
ANDREY FROLOV
Affiliation:
INNOPOLIS UNIVERSITY UNIVERSITETSKAYA STREET 1, INNOPOLIS 420500, RUSSIA E-mail: a.frolov.kpfu@gmail.com
MAXIM ZUBKOV*
Affiliation:
N.I. LOBACHEVSKY INSTITUTE OF MATHEMATICS AND MECHANICS KAZAN FEDERAL UNIVERSITY KREMLEVSKAYA 18, KAZAN 420008, RUSSIA
*
E-mail: maxim.zubkov@kpfu.ru
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Abstract

A low linear order with no computable copy constructed by C. Jockusch and R. Soare has Hausdorff rank equal to $2$. In this regard, the question arises, how simple can be a low linear order with no computable copy from the point of view of the linear order type? The main result of this work is an example of a low strong $\eta $-representation with no computable copy that is the simplest possible example.

Keywords

linear orderlow Turing degreeη-representationcomputable presentation

MSC classification

Primary: 03C57: Effective and recursion-theoretic model theory 03D45: Theory of numerations, effectively presented structures
Type
Article
Information
The Journal of Symbolic Logic , Volume 89 , Issue 1 , March 2024 , pp. 97 - 111
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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