A COMPUTABLE FUNCTOR FROM GRAPHS TO FIELDS
Author(s)SHLAPENTOKH, ALEXANDRA; Miller, Russell; Schoutens, Hans; Schoustens, Hans; Shlapentokh, Alexandra; Poonen, Bjorn; ... Show more Show less
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Fried and Kollár constructed a fully faithful functor from the category of graphs to the category of fields. We give a new construction of such a functor and use it to resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure S, there exists a countable field F of arbitrary characteristic with the same essential computable-model-theoretic properties as. 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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
The Journal of Symbolic Logic
Cambridge University Press (CUP)
MILLER, RUSSELL et al. “A COMPUTABLE FUNCTOR FROM GRAPHS TO FIELDS.” The Journal of Symbolic Logic 83, 1 (March 2018): 326–348 © 2018 The Association for Symbolic Logic