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A note on countable complete theories having three isomorphism types of countable models

Published online by Cambridge University Press:  12 March 2014

Robert E. Woodrow
Robert E. Woodrow*
Affiliation:
Simon Fraser University, Burnaby 2, British Colombia, Canada
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Abstract

With quantifier elimination and restriction of language to a binary relation symbol and constant symbols it is shown that countable complete theories having three isomorphism types of countable models are “essentially” the Ehrenfeucht example [4, §6].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 41 , Issue 3 , September 1976 , pp. 672 - 680
Copyright
Copyright © Association for Symbolic Logic 1976

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Footnotes

1

The author is indebted to Professor A. H. Lachlan for his guidance.

The author thanks the referee for suggestions to improve the clarity of exposition.

References

REFERENCES

[1] Benda, Miroslov, Remarks on countable models, Fundamenla Mathematicae, vol. 81 (1974), pp. 107–119.CrossRefGoogle Scholar
[2] Peretiatkin, M. G., On complete theories with a finite number of denumerable models, Algebra i Logika, vol. 12 (1973), pp. 550–576.Google Scholar
[3] Shoenfield, J. R., Mathematical logic, Addison-Wesley, Reading, Mass., 1967.Google Scholar
[4] Vaught, R. L., Denumerable models of complete theories, Infinitistic methods (Proceedings of a Symposium on the Foundations of Mathematics, Warsaw, 1959), Pergamon, Oxford; Paristwowe Wydawnictwo Naukowe, Warsaw, 1961, pp. 303–321.Google Scholar