Categoricity properties for computable algebraic fields
Denis R. Hirschfeldt, Ken Kramer, Russell Miller, Alexandra Shlapentokh · Transactions of the American Mathematical Society · 2014
We examine categoricity issues for computable algebraic fields. We give a structural criterion for relative computable categoricity 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 Π 4 0 \Pi ^0_4 -complete.