ℵ0-categorical modules
- 1 June 1975
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 40 (2) , 213-220
- https://doi.org/10.2307/2271901
Abstract
It is shown that the first-order theory ThR(A) of a countable module over an arbitrary countable ring R is ℵ0-categorical if and only if Ai finite, n ∈ ω, κi ≤ ω. Furthermore, ThR(A) is ℵ0-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.Keywords
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