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THE TREE OF TUPLES OF A STRUCTURE

Part of: Computability and recursion theory Model theory

Published online by Cambridge University Press:  07 September 2020

MATTHEW HARRISON-TRAINOR  and
ANTONIO MONTALBÁN
MATTHEW HARRISON-TRAINOR
Affiliation:
SCHOOL OF MATHEMATICS AND STATISTICS VICTORIA UNIVERSITY OF WELLINGTON, NEW ZEALAND and THE INSTITUTE OF NATURAL AND MATHEMATICAL SCIENCES MASSEY UNIVERSITY, NEW ZEALANDE-mail: matthew.harrisontrainor@vuw.ac.nzURL: http://homepages.ecs.vuw.ac.nz/~harrism1/
ANTONIO MONTALBÁN
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA, BERKELEY, CA, USAE-mail: Aantonio@math.berkeley.eduURL: http://www.math.berkeley.edu/~antonio/index.html
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Abstract

Our main result is that there exist structures which cannot be computably recovered from their tree of tuples. This implies that there are structures with no computable copies which nevertheless cannot code any information in a natural/functorial way.

Keywords

computable structure theoryback-and-forthcoding

MSC classification

Primary: 03D45: Theory of numerations, effectively presented structures
Secondary: 03C57: Effective and recursion-theoretic model theory
Type
Article
Information
The Journal of Symbolic Logic , Volume 87 , Issue 1 , March 2022 , pp. 21 - 46
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Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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