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Some questions concerning Hrushovski's amalgamation constructions

Part of: Model theory

Published online by Cambridge University Press:  07 October 2008

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

Keywords

amalgamation constructionstrongly minimalenvelopesfree amalgamationcollapsestandard system of geometries (codes)

MSC classification

Secondary: 03C45: Classification theory, stability and related concepts
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 7 , Issue 4 , October 2008 , pp. 793 - 823
Copyright
Copyright © Cambridge University Press 2008

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