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On Computable Field Embeddings and Difference Closed Fields

  Published:2017-05-25
 Printed: Dec 2017
  • Matthew Harrison-Trainor,
    Group in Logic and the Methodology of Science, University of California, Berkeley, California, USA
  • Alexander Melnikov,
    The Institute of Natural and Mathematical Sciences, Massey University, New Zealand
  • Russell Miller,
    Dept. of Mathematics, Queens College, City University of New York, New York, New York, USA
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Abstract

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: computable algebra, algebraic field, difference field, extension of automorphism computable algebra, algebraic field, difference field, extension of automorphism
MSC Classifications: 03D45, 03C57, 12Y05 show english descriptions Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]
Effective and recursion-theoretic model theory [See also 03D45]
Computational aspects of field theory and polynomials
03D45 - Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]
03C57 - Effective and recursion-theoretic model theory [See also 03D45]
12Y05 - Computational aspects of field theory and polynomials
 

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