Categoricity Properties for Computable Algebraic Fields
Status: published in the Transactions
of the American Mathematical
Society 367 (2015) 3981 - 4017.
version and preprint
Abstract. We examine categoricity issues for computable algebraic fields.
Such fields behave nicely for computable dimension: we show that they
cannot have finite computable dimension greater than 1. However,
they behave less nicely with regard to relative computable
categoricity: we give a structural criterion for relative computable
of these fields, and use it to construct a field that is computably
categorical, but not relatively computably categorical. Finally, we
show that computable categoricity for this class of fields is