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Ample Dividing

Published online by Cambridge University Press:  12 March 2014

David M. Evans
David M. Evans*
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, England, E-mail: [email protected]
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Abstract

We construct a stable one-based, trivial theory with a reduct which is not trivial. This answers a question of John B. Goode. Using this, we construct a stable theory which is n-ample for all natural numbers n, and does not interpret an infinite group.

Keywords

Stable theoriesreductstrivialityCM-triviality
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 4 , December 2003 , pp. 1385 - 1402
Copyright
Copyright © Association for Symbolic Logic 2003

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References

REFERENCES

[1] Baldwin, John T. and Shelah, Saharon, Randomness and semigenericity, Transactions of the American Mathematical Society, vol. 349 (1997), pp. 1359–1376.Google Scholar
[2] Baudisch, Andreas and Pillay, Anand, A free pseudospace, this Journal, vol. 65 (2000). pp. 443–463.Google Scholar
[3] Evans, David M., Trivial stable structures with non-trivial reducts, Unpublished notes, 05 2003.Google Scholar
[4] Evans, David M., Pillay, Anand, and Poizat, Bruno, Le groupe dans le groupe, Algebra i Logika, vol. 29 (1990), pp. 368–378, translated as A group in a group, Algebra and Logic , vol. 29 (1990), pp. 244–252.Google Scholar
[5] Goode, John B., Some trivial considerations, this Journal, vol. 56 (1991), pp. 624–631.Google Scholar
[6] Hodges, Wilfrid, Model theory, Cambridge University Press, 1997.Google Scholar
[7] Hrushovski, Ehud, A stable ℵ0-categorical pseudoplane, Unpublished notes, 1988.Google Scholar
[8] Hrushovski, Ehud, A new strongly minimal set, Annals of Pure and Applied Logic, vol. 62 (1993), pp. 147–166.Google Scholar
[9] Hrushovski, Ehud, Simplicity and the Lascar group, Unpublished notes, 12 1997.Google Scholar
[10] Pillay, Anand, The geometry of forking and groups of finite Morley rank, this Journal, vol. 60 (1995), pp. 1251–1259.Google Scholar
[11] Pillay, Anand, Geometric stability theory, Oxford University Press, 1996.Google Scholar
[12] Pillay, Anand, A note on CM-triviality and the geometry of forking, this Journal, vol. 65 (2000), pp. 474–480.Google Scholar
[13] Poizat, Bruno, Cours de théorie des modèles, Nur al-Mantiq wal-Ma'rifah, Villeurbanne, 1985.Google Scholar
[14] Poizat, Bruno, A course in model theory, Universitext, Springer-Verlag, New York, 2000, (English translation of [13]).Google Scholar