5 found
  1.  14
    A computable functor from graphs to fields.Russell Miller, Bjorn Poonen, Hans Schoutens & Alexandra Shlapentokh - 2018 - Journal of Symbolic Logic 83 (1):326-348.
    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${\cal S}$, 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 (...)
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    O-minimalism.Hans Schoutens - 2014 - Journal of Symbolic Logic 79 (2):355-409.
  3. Existentially closed models of the theory of artinian local rings.Hans Schoutens - 1999 - Journal of Symbolic Logic 64 (2):825-845.
    The class of all Artinian local rings of length at most l is ∀ 2 -elementary, axiomatised by a finite set of axioms Art l . We show that its existentially closed models are Gorenstein, of length exactly l and their residue fields are algebraically closed, and, conversely, every existentially closed model is of this form. The theory Got l of all Artinian local Gorenstein rings of length l with algebraically closed residue field is model complete and the theory Art (...)
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    University of California, San Diego, March 20–23, 1999.Julia F. Knight, Steffen Lempp, Toniann Pitassi, Hans Schoutens, Simon Thomas, Victor Vianu & Jindrich Zapletal - 1999 - Bulletin of Symbolic Logic 5 (3).
  5.  9
    Classifying singularities up to analytic extensions of scalars is smooth.Hans Schoutens - 2011 - Annals of Pure and Applied Logic 162 (10):836-852.
    The singularity space consists of all germs , with X a Noetherian scheme and x a point, where we identify two such germs if they become the same after an analytic extension of scalars. This is a complete, separable space for the metric given by the order to which jets agree after base change. In the terminology of descriptive set-theory, the classification of singularities up to analytic extensions of scalars is a smooth problem. Over , the following two classification problems (...)
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