A COMPUTABLE FUNCTOR FROM GRAPHS TO FIELDS
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Author(s)
SHLAPENTOKH, ALEXANDRA
Miller, Russell
Schoutens, Hans
Schoustens, Hans
Shlapentokh, Alexandra
Poonen, Bjorn
Date Issued
May 2018
Journal
The Journal of Symbolic Logic
Publisher
Cambridge University Press (CUP)
Citation
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
Version
Original manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1017/jsl.2017.50
