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Complete theories with only universal and existential axioms

Published online by Cambridge University Press:  12 March 2014

A. H. Lachlan
A. H. Lachlan*
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
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Abstract

Let T be a complete first-order theory over a finite relational language which is axiomatized by universal and existential sentences. It is shown that T is almost trivial in the sense that the universe of any model of T can be written . where F is finite and I 1, I 2, …, In are mutually indiscernible over F. Some results about complete theories with ∃∀-axioms over a finite relational language are also mentioned.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 3 , September 1987 , pp. 698 - 711
Copyright
Copyright © Association for Symbolic Logic 1987

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References

REFERENCES

[1] Hodkinson, I. M. and Macpherson, H. D., Relational structures determined by their finite induced substructures, this Journal (to appear).Google Scholar
[2] Macpherson, H. D., Graphs determined by their finite induced subgraphs, Journal of Combinatorial Theory, Series B, vol. 41 (1986), pp. 230–234.CrossRefGoogle Scholar
[3] Pouzet, M., Application d'une propriété combinatoire des parties d'un ensemble aux groupes et aux relations, Mathematische Zeitschrift, vol. 150 (1976), pp. 117–134.CrossRefGoogle Scholar
[4] Shelah, S., Classification theory and the number of non-isomorphic models, North-Holland, Amsterdam, 1978.Google Scholar