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COMPUTABLE FUNCTORS AND EFFECTIVE INTERPRETABILITY

Published online by Cambridge University Press:  25 January 2017

MATTHEW HARRISON-TRAINOR ,
ALEXANDER MELNIKOV ,
RUSSELL MILLER  and
ANTONIO MONTALBÁN
MATTHEW HARRISON-TRAINOR
Affiliation:
GROUP IN LOGIC AND THE METHODOLOGY OF SCIENCE UNIVERSITY OF CALIFORNIA BERKELEY, CA, USA E-mail: matthew.h-t@math.berkeley.edu URL: http://math.berkeley.edu/∼mattht
ALEXANDER MELNIKOV
Affiliation:
THE INSTITUTE OF NATURAL AND MATHEMATICAL SCIENCES MASSEY UNIVERSITY, NEW ZEALAND E-mail: alexander.g.melnikov@gmail.com URL: https://dl.dropboxusercontent.com/u/4752353/homepage/index.html
RUSSELL MILLER
Affiliation:
MATHEMATICS DEPT., QUEENS COLLEGE; PH.D. PROGRAMS IN MATHEMATICS & COMPUTER SCIENCE GRADUATE CENTER, CITY UNIVERSITY OF NEW YORK, USA E-mail: russell.miller@qc.cuny.edu URL: http://qcpages.qc.cuny.edu/∼rmiller
ANTONIO MONTALBÁN
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA BERKELEY, CA, USA E-mail: antonio@math.berkeley.edu URL: www.math.berkeley.edu/∼antonio
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Abstract

Our main result is the equivalence of two notions of reducibility betweenstructures. One is a syntactical notion which is an effective version ofinterpretability as in model theory, and the other one is a computational notionwhich is a strengthening of the well-known Medvedev reducibility. We extend ourresult to effective bi-interpretability and also to effective reductions betweenclasses of structures.

Keywords

computable functoreffective interpretabilityƩ-reducibility

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 1 , March 2017 , pp. 77 - 97
Copyright
Copyright © The Association for Symbolic Logic 2017 

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References

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