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Some questions concerning Hrushovski's amalgamation constructions

Published online by Cambridge University Press:  07 October 2008

Assaf Hasson
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St Giles', Oxford OX1 3LB, UK

Abstract

In order to construct a counterexample to Zilber's conjecture—that a strongly minimal set has a degenerate, affine or field-like geometry—Ehud Hrushovski invented an amalgamation technique which has yielded all the exotic geometries so far. We shall present a framework for this construction in the language of standard geometric stability and show how some of the recent constructions fit into this setting. We also ask some fundamental questions concerning this method.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2008

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