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ℵ0-categorical modules

Published online by Cambridge University Press:  12 March 2014

Walter Baur
Walter Baur*
Affiliation:
Yale University, New Haven, Connecticut 06520
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 40 , Issue 2 , June 1975 , pp. 213 - 220
Copyright
Copyright © Association for Symbolic Logic 1975

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References

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