On reducts of Hrushovski's construction: - the non-collapsed case

Assaf Hasson, Omer Mermelstein

Research output: Working paper/PreprintPreprint

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Abstract

We show that the rank {\omega} structure obtained by the non-collapsed version of Hrushovski's amalgamation construction has a proper reduct. We show that this reduct is the Fraïssé-Hrushovski limit of its own age with respect to a pre-dimension function generalising Hrushovski's pre-dimension function. It follows that this reduct has a unique regular type of rank {\omega}, and we prove that its geometry is isomorphic to the geometry of the generic type in the original structure. We ask whether our reduct is bi-interpretable with the original structure and whether it, too, has proper reducts with the same geometry.
Original languageEnglish
StatePublished - 2013

Publication series

NameArxiv preprint

Keywords

  • Mathematics - Logic
  • 03C45
  • 03C30

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