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On minimal structures

Published online by Cambridge University Press:  12 March 2014

Oleg V. Belegradek*
Affiliation:
Department of Mathematics, Kemerovo State University, Kemerovo, Russia 650043, E-mail: [email protected]

Abstract

For any countable transitive complete theory T with infinite models and the finite model property, we construct a minimal structure M such that the theory of M is small if and only if T is small, and is λ-stable if and only if T is λ-stable. This gives a series of new examples of minimal structures.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1] Baldwin, J. T. and Lachlan, A. H., On strongly minimal sets, this Journal, vol. 36 (1971), pp. 7996.Google Scholar
[2] Marsh, W. E., On ω1-categorical and not ω-categorical theories, Ph.D. thesis , Dartmouth College, 1966.Google Scholar
[3] Prest, M., Model theory and modules, London Mathematical Society Lecture Notes Series, no. 130, Cambridge University Press, Cambridge, 1988.Google Scholar
[4] Zil'ber, B. I. and Smurov, V. P., On minimal structures, Ninth all-union conference on mathematical logic, Nauka, Leningrad, 1988, in Russian, p. 65.Google Scholar