$\aleph_0$-Categorical Modules
Baur, Walter
J. Symbolic Logic, Tome 40 (1975) no. 1, p. 213-220 / Harvested from Project Euclid
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It is shown that the first-order theory $\mathrm{Th}_R(A)$ of a countable module over an arbitrary countable ring $R$ is $\aleph_0$-categorical if and only if $A \cong \bigoplus_{t < n}A_i^{(\kappa_i)}, A_i$ finite, $n \in \omega, \kappa_i \leq \omega$. Furthermore, $\mathrm{Th}_R(A)$ is $\aleph_0$-categorical for all $R$-modules $A$ if and only if $R$ is finite and there exist only finitely many isomorphism classes of indecomposable $R$-modules.
Publié le : 1975-06-14
Classification:  
@article{1183739382,
     author = {Baur, Walter},
     title = {$\aleph\_0$-Categorical Modules},
     journal = {J. Symbolic Logic},
     volume = {40},
     number = {1},
     year = {1975},
     pages = { 213-220},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183739382}
}

Baur, Walter. $\aleph_0$-Categorical Modules. J. Symbolic Logic, Tome 40 (1975) no. 1, pp.  213-220. http://gdmltest.u-ga.fr/item/1183739382/