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Pseudo-finite homogeneity and saturation

Published online by Cambridge University Press:  12 March 2014

Jörg Flum  and
Martin Ziegler
Jörg Flum
Affiliation:
Institut Für Mathematische Logik, Universität Freiburg, Eckestr. 1, 79104 Freiburg, Germany, E-mail: [email protected]
Martin Ziegler
Affiliation:
Institut Für Mathematische Logik, Universität Freiburg, Eckestr. 1, 79104 Freiburg, Germany, E-mail: [email protected]
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Abstract

When analyzing database query languages a roperty, of theories, the pseudo-finite homogeneity property, has been introduced and applied (cf. [3]). We show that a stable theory has the pseudo-finite homogeneity property just in case its expressive power for finite states is bounded. Moreover, we introduce the corresponding pseudo-finite saturation property and show that a theory fails to have the finite cover property if and only if it has the pseudo-finite saturation property.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 4 , December 1999 , pp. 1689 - 1699
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

[1]Baldwin, J.T. and Benedikt, M., Stability theory, permutations of indiscernibles, and embedded finite models, preprint.Google Scholar
[2]Baldwin, J.T. and Kueker, D. W., Ramsey quantifiers and the finite cover property, Pacific Journal of Mathematics, vol. 90 (1980), pp. 11–19.CrossRefGoogle Scholar
[3]Belegradek, O.V., Stolboushkin, A.P., and Taitslin, M.A., Extended order-generic queries, preprint.Google Scholar
[4]Belegradek, O.V., Stolboushkin, A.P., and Taitslin, M.A., On problems of databases over a fixed infinite universe, Helena Rasiowa in memoriam, Banach Center Publications, vol. 46, 1999, pp. 23–62.Google Scholar
[5]Benedikt, M., Dong, G., Libkin, L., and Wong, L., Relational expressive power of constraint query languages, Journal of the ACM, to appear. Extended abstract in Proceedings of ACM Symposium on Principles of Database Systems, 1996, 5–16.Google Scholar
[6]Benedikt, M. and Libkin, L., On the structure of queries in constraint query languages, Proceedings of IEEE Symposium on Logic in Computer Science (1996), pp. 25–34.Google Scholar
[7]Casanovas, E. and Ziegler, M., Stable theories with a new predicate, preprint.Google Scholar
[8]Shelah, S., Classification theory, North-Holland, 1990.Google Scholar