Computable Categoricity for Algebraic Fields with Splitting Algorithms
Logic
2018-02-12 v1 Commutative Algebra
Number Theory
Abstract
A computably presented algebraic field has a \emph{splitting algorithm} if it is decidable which polynomials in are irreducible there. We prove that such a field is computably categorical iff it is decidable which pairs of elements of belong to the same orbit under automorphisms. We also show that this criterion is equivalent to the relative computable categoricity of .
Cite
@article{arxiv.1111.1205,
title = {Computable Categoricity for Algebraic Fields with Splitting Algorithms},
author = {Russell Miller and Alexandra Shlapentokh},
journal= {arXiv preprint arXiv:1111.1205},
year = {2018}
}