Generic stability and stability

Hans Adler; Enrique Casanovas; Anand Pillay

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arXiv · 1210.5957

Generic stability and stability

Hans Adler·Enrique Casanovas·Anand Pillay

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Abstract

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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BibTeX RIS

Hans Adler, Enrique Casanovas, Anand Pillay. 2012-10-22. Generic stability and stability. https://arxiv.org/abs/1210.5957

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