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Preprint Number 521

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521. Hans Adler, Enrique Casanovas and Anand Pillay
Generic stability and stability

Submission date: 21 October 2012.


We prove two results about generically stable types p in arbitrary theories. The first, on existence of strong germs, generalizes results from D. Haskell, E. Hrushovski and D. Macpherson on stably dominated types. The second is an equivalence of forking and dividing, assuming generic stability of p^(m) for all m. We use the latter result to answer in full generality a question posed by Hasson and Onshuus: If p(x)\in S(B) is stable and does not fork over A then p\restriction A is stable. (They had solved some special cases.)

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Full text arXiv 1210.5957: pdf, ps.

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