Ehud Hrushovski

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We give a proof of the geometric Mordell-Lang conjecture, in any characteristic. Our method involves a model-theoretic analysis of the kernel of Manin’s homomorphism and of a certain analog in characteristic p. Department of Mathematics, Massachusetts Institute of Technology, 2-277, Cambridge, Massachusetts 02139 Current address: Department of Mathematics,(More)
Finite structures with few types / by Gregory Cherlin and Ehud Hrushovski. p. cm.– (Annals of mathematics studies ; no. 152) Includes bibliographical references and index. The publisher acknowledges the authors for providing the camera-ready copy from which this book was printed.
We lay down some elements of a geometry based on difference equations. Various constructions of algebraic geometry are shown to have meaningful analogs: dimensions, blowingup, moving lemmas. Analogy aside, the geometry of difference equations has two quite different functorial connections with ordinary algebraic geometry. On the one hand, a difference(More)
We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of Denef,Loeser, Cluckers. The method depends on an analysis of definable sets up to definable bijections. We obtain a(More)
This book addresses a gap in the model-theoretic understanding of valued fields that has, until now, limited the interactions of model theory with geometry. It contains significant developments in both pure and applied model theory. Part I of the book is a study of stably dominated types. These form a subset of the type space of a theory that behaves in(More)
This paper contains a series of easy constructions and observations relating to the Lascar group and to simple theories. 1 In x1 we review basic model theoretic ideas, relating mostly to model completion and saturated models. We do so in order to introduce a framework very slightly more general than the usual rst-order one that will be useful to us, and(More)
A strongly minimal structure D is called unimodular if any two finite-to-one maps with the same domain and range have the same degree; that is if/4: (/-»• V is everywhere fc4-to-l, then kx = kc,. THEOREM. Unimodular strongly minimal structures are locally modular. This extends Zil'ber's theorem on locally finite strongly minimal sets, Urbanik's theorem on(More)