A COMPUTABLE FUNCTOR FROM GRAPHS TO FIELDS
Keyword(s):
AbstractFried 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${\cal S}$, there exists a countable field${\cal F}$of arbitrary characteristic with the same essential computable-model-theoretic properties as${\cal S}$. 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.
2004 ◽
Vol 69
(4)
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pp. 1117-1142
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2007 ◽
Vol 72
(3)
◽
pp. 1041-1054
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Keyword(s):