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On Computable Field Embeddings and Difference Closed Fields

Published online by Cambridge University Press:  20 November 2018

Matthew Harrison-Trainor ,
Alexander Melnikov  and
Russell Miller
Matthew Harrison-Trainor
Affiliation:
Group in Logic and the Methodology of Science, University of California, Berkeley, USA e-mail: matthew.h-t@berkeley.edu
Alexander Melnikov
Affiliation:
The Institute of Natural and Mathematical Science, Massey University, New Zealand e-mail: alexander.g.melnikov@gmail.com
Russell Miller
Affiliation:
Dept. of Mathematics, Queens College, - Ph.D. Programs inMathematics - Computer Science, Graduate Center, City University of New York, USA e-mail: Russell.Miller@qc.cuny.edu
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Abstract

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We investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of computable difference fields into computable difference closed fields.

Keywords

03D4503C5712Y05computable algebraalgebraic fielddifference fieldextension of automorphism
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 6 , 01 December 2017 , pp. 1338 - 1363
Copyright
Copyright © Canadian Mathematical Society 2016

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