Categoricity Properties for Computable Algebraic Fields

Details Categoricity Properties for Computable Algebraic Fields Categoricity Properties for Computable Algebraic Fields

2011-11-04

arxiv.org/abs/1111.1211v1

Mathematics

Logic

Scientific paper

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 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 $\Pi^0_4$-complete.

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