@article {IOPORT.06005014,
    author       = {Ivanov, Aleksander},
    title        = {Degrees of isomorphism types and countably categorical groups.},
    year         = {2012},
    journal      = {Archive for Mathematical Logic},
    volume       = {51},
    number       = {1-2},
    issn         = {0933-5846},
    pages        = {93-98},
    publisher    = {Springer-Verlag, Berlin},
    doi          = {10.1007/s00153-011-0255-6},
    abstract     = {A countable structure with the universe $\omega$ is said to be of (Turing) degree $\bold{d}$ iff its atomic diagram has degree $\bold{d}$. By the spectrum $\mathrm{Spec}(\mathcal{M})$ of a structure $\mathcal{M}$ we mean the set of degrees of structures isomorphic to $\mathcal{M}$. If $\mathrm{Spec}(\mathcal{M})$ has a least element $\bold{d}$ then $\mathcal{M}$ is said to have degree $\bold{d}$; otherwise, we say that $\mathcal{M}$ has no degree. The main result of the paper under review is following: Theorem. (i) For every Turing degree $\bold{d}$ there is a 2-step nilpotent group $\mathfrak{G}$ of exponent four so that $\mathfrak{G}$ has a countably categorical theory submodel complete (i.e., with quantifier elimination) theory and has degree $\bold{d}$. (ii) There is a 2-step nilpotent group $\mathfrak{G}$ of exponent four so that $\mathfrak{G}$ has a countably categorical theory submodel complete theory and has no degree. The author uses the Fra\"{\i}ss\'e method for constructing both series of examples.},
    reviewer     = {Vadim Puzarenko (Novosibirsk)},
    identifier   = {06005014},
}