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Lattice of algebraically closed sets in one-based theories1

Published online by Cambridge University Press:  12 March 2014

Lee Fong Low
Lee Fong Low*
Affiliation:
26 Beacon Street, Apartment 16C, Burlington, Massachusetts 01803
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Abstract

Let T be a one-based theory. We define a notion of width, in the case of T having the finiteness property, for the lattice of finitely generated algebraically closed sets and prove

Theorem. Let T be one-based with the finiteness property. If T is of bounded width, then every type in T is nonorthogonal to a weight one type. If T is countable, the converse is true.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 1 , March 1994 , pp. 311 - 321
Copyright
Copyright © Association for Symbolic Logic 1994

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Footnotes

1

This work forms a chapter of the author's dissertation, written under the direction of Professor Anand Pillay at the University of Notre Dame, 1992.

References

REFERENCES

[BoPo] Bouscaren, E. and Poizat, B., Des belles paires aux beaux uples, this Journal, vol. 53 (1988), pp. 434–442.Google Scholar
[EPPo] Evans, D., Pillay, A., and Poizat, B., A group in a group, Algebra i Logika, vol. 3 (1990), pp. 368–378.Google Scholar
[G] Goode, J. B., Some trivial considerations, this Journal, vol. 56 (1991), pp. 624–631.Google Scholar
[H] Hrushovski, E., Finitely based theories, this Journal, vol. 54 (1989), pp. 221–225.Google Scholar
[HP] Hrushovski, E. and Pillay, P., Weakly normal groups, Logic Colloquium' 85, North-Holland, Amsterdam, 1986, pp. 233–244.Google Scholar
[Pr] Prest, M., Model theory of modules, Cambridge University Press, Longon and New York, 1988.CrossRefGoogle Scholar
[Z] Ziegler, M., Model theory of modules, Annals of Pure and Applied Logic, vol. 26 (1984), pp. 149–213.CrossRefGoogle Scholar