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Isolated types in a weakly minimal set

Published online by Cambridge University Press:  12 March 2014

Steven Buechler*
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720

Abstract

Theorem A. Let T be a small superstable theory, A a finite set, and ψ a weakly minimal formula over A which is contained in some nontrivial type which does not have Morley rank. Then ψ is contained in some nonalqebraic isolated type over A.

As an application we prove

Theorem B. Suppose that T is small and superstable, A is finite, and there is a nontrivial weakly minimal type p ∈ S(A) which does not have Morley rank. Then the prime model over A is not minimal over A.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1987

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References

REFERENCES

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