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On one-based theories

Published online by Cambridge University Press:  12 March 2014

E. Bouscaren  and
E. Hrushovski
E. Bouscaren
Affiliation:
Université Paris7, CNRS URA 753-UFR de Mathématiques, 75251 Paris Cedex 05France
E. Hrushovski
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Department of Mathematics, Hebrew University, Jerusalem 91904, Israel
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Extract

We know from [H1], [H2] that in a stable theory, given a nontrivial locally modular regular type q, one can define a group with generic domination equivalent to q, and that the dependence relation on q can be analyzed in terms of this group. In a stable one-based theory, every regular type is locally modular; hence, this result holds for every nontrivial regular type. We show here that, in fact, in a stable one-based theory, a similar type of construction can be done without the assumption of regularity. More precisely, we show that for any type q, the nontrivial part of q can be analyzed by generics of groups and that any nontrivial relation can be described by affine relations (Theorem A).

This construction is then used to answer a question about homogeneity in pairs of models which is still open in the case of arbitrary stable theories (Theorem C).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 2 , June 1994 , pp. 579 - 595
Copyright
Copyright © Association for Symbolic Logic 1994

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References

REFERENCES

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