8 found
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  1.  4
    Effective Categoricity of Equivalence Structures.Wesley Calvert, Douglas Cenzer, Valentina Harizanov & Andrei Morozov - 2006 - Annals of Pure and Applied Logic 141 (1):61-78.
    We investigate effective categoricity of computable equivalence structures . We show that is computably categorical if and only if has only finitely many finite equivalence classes, or has only finitely many infinite classes, bounded character, and at most one finite k such that there are infinitely many classes of size k. We also prove that all computably categorical structures are relatively computably categorical, that is, have computably enumerable Scott families of existential formulas. Since all computable equivalence structures are relatively categorical, (...)
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  2.  8
    The Isomorphism Problem for Computable Abelian P-Groups of Bounded Length.Wesley Calvert - 2005 - Journal of Symbolic Logic 70 (1):331 - 345.
    Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out a sequence of examples. We follow recent work by Goncharov and Knight in using the degree of the isomorphism problem for a class to distinguish classifiable classes from non-classifiable. In (...)
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  3.  4
    The Isomorphism Problem for Classes of Computable Fields.Wesley Calvert - 2004 - Archive for Mathematical Logic 43 (3):327-336.
    Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out several examples. One motivation is to see whether some classes whose set of countable members is very complex become classifiable when we consider only computable members. We follow recent work (...)
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  4. On Three Notions of Effective Computation Over R.Wesley Calvert - unknown
     
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  5.  3
    Effective Categoricity of Abelian P -Groups.Wesley Calvert, Douglas Cenzer, Valentina S. Harizanov & Andrei Morozov - 2009 - Annals of Pure and Applied Logic 159 (1-2):187-197.
    We investigate effective categoricity of computable Abelian p-groups . We prove that all computably categorical Abelian p-groups are relatively computably categorical, that is, have computably enumerable Scott families of existential formulas. We investigate which computable Abelian p-groups are categorical and relatively categorical.
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  6.  19
    Classification From a Computable Viewpoint.Wesley Calvert & Julia F. Knight - 2006 - Bulletin of Symbolic Logic 12 (2):191-218.
  7.  13
    Computable Trees of Scott Rank [Image] , and Computable Approximation.Wesley Calvert, Julia F. Knight & Jessica Millar - 2006 - Journal of Symbolic Logic 71 (1):283 - 298.
    Makkai [10] produced an arithmetical structure of Scott rank $\omega _{1}^{\mathit{CK}}$. In [9]. Makkai's example is made computable. Here we show that there are computable trees of Scott rank $\omega _{1}^{\mathit{CK}}$. We introduce a notion of "rank homogeneity". In rank homogeneous trees, orbits of tuples can be understood relatively easily. By using these trees, we avoid the need to pass to the more complicated "group trees" of [10] and [9]. Using the same kind of trees, we obtain one of rank (...)
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  8.  6
    PAC Learning, VC Dimension, and the Arithmetic Hierarchy.Wesley Calvert - 2015 - Archive for Mathematical Logic 54 (7-8):871-883.