Computable categoricity for algebraic fields with splitting algorithms
Russell Miller, Alexandra Shlapentokh · Transactions of the American Mathematical Society · 2014
A computably presented algebraic field F F has a splitting algorithm if it is decidable which polynomials in F [ X ] F[X] are irreducible there. We prove that such a field is computably categorical iff it is decidable which pairs of elements of F F belong to the same orbit under automorphisms. We also show that this criterion is equivalent to the relative computable categoricity of F F .