Some questions concerning Hrushovski's amalgamation constructions

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3 Scopus citations

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.

Original languageEnglish
Pages (from-to)793-823
Number of pages31
JournalJournal of the Institute of Mathematics of Jussieu
Volume7
Issue number4
DOIs
StatePublished - 20 Oct 2008

Keywords

  • Amalgamation construction
  • Collapse
  • Envelopes
  • Free amalgamation
  • Standard system of geometries (codes)
  • Strongly minimal

ASJC Scopus subject areas

  • General Mathematics

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