Switch to: Citations

Add references

You must login to add references.
  1. Degrees of Categoricity and the Hyperarithmetic Hierarchy.Barbara F. Csima, Johanna N. Y. Franklin & Richard A. Shore - 2013 - Notre Dame Journal of Formal Logic 54 (2):215-231.
    We study arithmetic and hyperarithmetic degrees of categoricity. We extend a result of E. Fokina, I. Kalimullin, and R. Miller to show that for every computable ordinal $\alpha$, $\mathbf{0}^{}$ is the degree of categoricity of some computable structure $\mathcal{A}$. We show additionally that for $\alpha$ a computable successor ordinal, every degree $2$-c.e. in and above $\mathbf{0}^{}$ is a degree of categoricity. We further prove that every degree of categoricity is hyperarithmetic and show that the index set of structures with degrees (...)
    Direct download (6 more)  
    Export citation  
    Bookmark   7 citations  
  • Degrees of Categoricity of Computable Structures.Ekaterina B. Fokina, Iskander Kalimullin & Russell Miller - 2010 - Archive for Mathematical Logic 49 (1):51-67.
    Defining the degree of categoricity of a computable structure ${\mathcal{M}}$ to be the least degree d for which ${\mathcal{M}}$ is d-computably categorical, we investigate which Turing degrees can be realized as degrees of categoricity. We show that for all n, degrees d.c.e. in and above 0 (n) can be so realized, as can the degree 0 (ω).
    Direct download (4 more)  
    Export citation  
    Bookmark   10 citations  
  • Computably Isometric Spaces.Alexander G. Melnikov - 2013 - Journal of Symbolic Logic 78 (4):1055-1085.