A Computable Functor From Graphs to Fields

Russell Miller; Bjorn Poonen; Hans Schoutens; Alexandra Shlapentokh

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arXiv · 1510.07322

A Computable Functor From Graphs to Fields

Russell Miller·Bjorn Poonen·Hans Schoutens·Alexandra Shlapentokh

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Abstract

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.

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BibTeX RIS

Russell Miller, Bjorn Poonen, Hans Schoutens, Alexandra Shlapentokh. 2015-10-25. A Computable Functor From Graphs to Fields. https://arxiv.org/abs/1510.07322

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