Computable Categoricity for Algebraic Fields with Splitting Algorithms

Details Computable Categoricity for Algebraic Fields with Splitting Algorithms Computable Categoricity for Algebraic Fields with Splitting Algorithms

2011-11-04

arxiv.org/abs/1111.1205v1

Mathematics

Logic

Scientific paper

A computably presented algebraic field $F$ has a \emph{splitting algorithm}
if it is decidable which polynomials in $F[X]$ are irreducible there. We prove
that such a field is computably categorical iff it is decidable which pairs of
elements of $F$ belong to the same orbit under automorphisms. We also show that
this criterion is equivalent to the relative computable categoricity of $F$.

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