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A structure theorem for strongly abelian varieties with few models

Published online by Cambridge University Press:  12 March 2014

Bradd Hart  and
Matthew Valeriote
Bradd Hart
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720 Department of Mathematics, Mcmaster University, Hamilton, Ontario L8S 4K1, Canada
Matthew Valeriote
Affiliation:
Department of Mathematics, Mcmaster University, Hamilton, Ontario L8S 4K1, Canada
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Extract

By a variety, we mean a class of structures in some language containing only function symbols which is equationally defined or equivalently is closed under homomorphisms, submodels and products.

If K is a class of -structures then I(K, λ) denotes the number of nonisomorphic models in K of cardinality λ. When we say that K has few models, we mean that I(K,λ) < 2λ for some λ > ∣∣. If I(K,λ) = 2λ for all λ > ∣∣, then we say K has many models. In [9] and [10], Shelah has shown that for an elementary class K, having few models is a strong structural condition.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 3 , September 1991 , pp. 832 - 852
Copyright
Copyright © Association for Symbolic Logic 1991

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References

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