ℵ0-categorical modules

Journal of Symbolic Logic 40 (2):213 - 220 (1975)
It is shown that the first-order theory Th R (A) of a countable module over an arbitrary countable ring R is ℵ 0 -categorical if and only if $A \cong \bigoplus_{t finite, n ∈ ω, κ i ≤ ω. Furthermore, Th R (A) is ℵ 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
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DOI 10.2307/2271901
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References found in this work BETA
Model-Completions and Modules.Paul Eklof & Gabriel Sabbagh - 1971 - Annals of Mathematical Logic 2 (3):251-295.
The Elementary Theory of Abelian Groups.Paul C. Eklof & Edward R. Fischer - 1972 - Annals of Mathematical Logic 4 (2):115-171.

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Model Theory of Modules.Martin Ziegler - 1984 - Annals of Pure and Applied Logic 26 (2):149-213.

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