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Stable structures with few substructures

Published online by Cambridge University Press:  12 March 2014

Michael C. Laskowski  and
Laura L. Mayer
Michael C. Laskowski
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA, E-mail: [email protected]
Laura L. Mayer
Affiliation:
Department of Mathematical and Computer Sciences, Loyola University Chicago, Chicago, IL 60626, USA, E-mail: [email protected]
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Abstract

A countable, atomically stable structure in a finite, relational language has fewer than 2ω non-isomorphic substructures if and only if is cellular. An example shows that the finiteness of the language is necessary.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 3 , September 1996 , pp. 985 - 1005
Copyright
Copyright © Association for Symbolic Logic 1996

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References

REFERENCES

[1]Litman, A. and Shelah, S., Models with few isomorphic expansions, Israel Journal of Mathematics, vol. 28 (1977), pp. 331–338.CrossRefGoogle Scholar
[2]MacPherson, D. and Schmerl, J., Binary relational structures having only countably many non-isomorphic substructures, this Journal, vol. 51 (1991), pp. 876–884.Google Scholar
[3]Morley, M., Categoricity in power, Transactions of the American Mathematical Society, vol. 114 (1965), pp. 514–538.CrossRefGoogle Scholar