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Preprint Number 949
949. Russell Miller, Bjorn Poonen, Hans Schoutens, and Alexandra Shlapentokh
A Computable Functor From Graphs to Fields
Submission date: 25 October 2015.
We construct a fully faithful functor from the category of graphs to the category of fields. Using this functor, we resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure S, there exists a countable field F with the same essential computable-model-theoretic properties as S. Along the way, we develop a new computable category theory, and prove that our functor and its partially-defined inverse (restricted to the categories of countable graphs and countable fields) are computable functors.
Mathematics Subject Classification: 03C57 (Primary) 03D45, 12L12, 18A15, 08A35 (Secondary)
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