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Relational structures determined by their finite induced substructures

Published online by Cambridge University Press:  12 March 2014

I. M. Hodkinson and
H. D. Macpherson
I. M. Hodkinson
Affiliation:
School of Mathematical Sciences, Queen Mary College, London EL 4NS, England
H. D. Macpherson*
Affiliation:
New Hall, Cambridge CB3 ODF, England
*
Mathematical Institute, 24–29 St. Giles, Oxford OX1 3LB, England
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Abstract

A countably infinite relational structure M is called absolutely ubiquitous if the following holds: whenever N is a countably infinite structure, and M and N have the same isomorphism types of finite induced substructures, there is an isomorphism from M to N. Here a characterisation is given of absolutely ubiquitous structures over languages with finitely many relation symbols. A corresponding result is proved for uncountable structures.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 53 , Issue 1 , March 1988, pp. 222 - 230
Copyright
Copyright © Association for Symbolic Logic 1988

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References

REFERENCES

[1] Birch, B. J. et al., On the orbit sizes of permutation groups containing elements separating finite subsets, Bulletin of the Australian Mathematical Society, vol. 14 (1976), pp. 7–10.CrossRefGoogle Scholar
[2] Chang, C. C. and Keisler, H. J., Model theory, North-Holland, Amsterdam, 1973.Google Scholar
[3] Hodges, W. A., Building models by games, Cambridge University Press, Cambridge, 1985.Google Scholar
[4] Lachlan, A. H., Complete theories with only existential and universal axioms, this Journal, vol. 52 (1987), pp. 698–711.Google Scholar
[5] Macpherson, H. D., Graphs determined by their finite induced subgraphs, Journal of Combinatorial Theory Series B, vol. 41 (1986), pp. 230–234.CrossRefGoogle Scholar
[6] Morley, M., Categoricity in power, Transactions of the American Mathematical Society, vol. 114 (1965), pp. 514–538.CrossRefGoogle Scholar
[7] Pillay, A., An introduction to stability theory, Clarendon Press, Oxford, 1983.Google Scholar
[8] Pouzet, M., Application d’une propriété combinatoire des parties d'un ensemble aux groupes et aux relations, Mathematische Zeitschrift, vol. 150 (1976), pp. 117–134.CrossRefGoogle Scholar
[9] Sacks, G. E., Saturated model theory, Benjamin, Reading, Massachusetts, 1972.Google Scholar