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Categoricity Properties for Computable Algebraic Fields | | Denis Hirschfeldt
; Ken Kramer
; Russell Miller
; Alexandra Shlapentokh
; | | Date: |
4 Nov 2011 | | 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 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. | | Source: | arXiv, 1111.1211 | | Services: | Forum | Review | PDF | Favorites | |
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