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Hanf number of omitting type for simple first-order theories

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah*
Affiliation:
Hebrew University, Jerusalem, Israel

Abstract

Let T be a complete countable first-order theory such that every ultrapower of a model of T is saturated. If T has a model omitting a type p in every cardinality < ℶ, then T has a model omitting p in every cardinality. There is also a related theorem, and an example showing the ℶ cannot be improved.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1979

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References

REFERENCES

[1]Erdös, P., Hajnal, A. and Rado, R., Partition relations for cardinal numbers, Acta Mathematica, vol. 16 (1965), pp. 93196.Google Scholar
[2]Chang, C. C. and Keisler, H. J., Model theory, North-Holland, Amsterdam, 1973.Google Scholar
[3]Morley, M. D., Omitting classes of elements, The theory of models, Proceedings of the Berkeley Symposium, 1962 (Addison, , Henkin, and Tarski, , Editors), North-Holland, Amsterdam, 1965, pp. 256273.Google Scholar
[4]Morley, M.D. and Vaught, R. L., Homogeneous universal models, Mathematica Scandinavia, vol. 11 (1962), pp. 3757.CrossRefGoogle Scholar
[5]Shelah, S., On the number of nonisomorphic models of a theory in a cardinality, abstract, Notices of the American Mathematical Society, vol. 17 (1970), p. 576.Google Scholar
[6]Shelah, S., Classification theory and the number of non-isomorphic models, North-Holland, Amsterdam, 1978.Google Scholar
[7]Shelah, S., Stability, superstability and the f.c.p., model theoretic properties of formulas in first-order theory, Annals of Mathematical Logic, vol. 3 (1971), pp. 271362.CrossRefGoogle Scholar