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On the number of minimal models

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah*
Affiliation:
Hebrew University, Jerusalem, Israel

Abstract

Answering a problem of Fuhrken we prove that for every κ, 1 ≤ κ ≤ ℵ0, there is a (countable) complete theory T, with no prime model, and exactly κ minimal models (up to isomorphism).

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1978

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References

REFERENCES

[1]Fuhrken, G., Minimal und Primmodelle, Archiv für mathematische Logik und Gundlagenforschung, vol. 9 (1963), pp. 311.CrossRefGoogle Scholar
[2]Marcus, L., A type-open minimal model, Archiv für mathematische Logik und Grundlagenforschung.Google Scholar
[3]Morley, M., The number of countable models, this Journal, vol. 35 (1970), pp. 1418.Google Scholar
[4]Shelah, S., Some remarks in model theory, Notices of the American Mathematical Society, vol. 23 (1976), p. A289.Google Scholar