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Modules with regular generic types part iv

Published online by Cambridge University Press:  12 March 2014

Ivo Herzog  and
Philipp Rothmaler
Ivo Herzog*
Affiliation:
Department of Mathematics, University of California, Irvine, California 92717
Philipp Rothmaler
Affiliation:
Institut für Logik, Universität Kiel, W-2300 Kiel 1, Germany
*
Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254, E-mail: herzog@brandeis.bitnet
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Extract

In this paper, we continue the line of investigation undertaken in [HR], with which we assume familiarity. For a comprehensive reference we refer the reader to [P]. The authors would like to thank each other for their light spirit and good humor.

Pillay and Prest [PP, Proposition 7.10] have shown that a module M of U-rank 1 which is not totally transcendental may be decomposed as M = Ml ⊕ Mu, where Ml, ⊨ Th(M) omits the unlimited type and Mu imbeds purely into a model of the unlimited part Tu, of T = Th(M). We devote the first section of this paper to a generalization of this result to the case when T has a regular generic and m-dim(M) = 1. (Note that m-dim(M) = 0 implies M is totally transcendental, in which case a general decomposition theorem was proved by Garavaglia [G].)

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 1 , March 1992 , pp. 193 - 199
Copyright
Copyright © Association for Symbolic Logic 1992

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References

REFERENCES

[B]Buechler, S., The classification of small weakly minimal sets. III: Modules, this Journal, vol. 53 (1988), pp. 975–979.Google Scholar
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[PP]Pillay, A. and Prest, M., Modules and stability theory, Transactions of the American Mathematical Society, vol. 300 (1987), pp. 641–662.CrossRefGoogle Scholar
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