Reducts of Hrushovski's constructions of a higher geometrical arity

Assaf Hasson, Omer Mermelstein

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Abstract

Let Mn denote the structure obtained from Hrushovski's (non-collapsed) construction with an n-ary relation and PG(Mn) its associated pregeometry. It was shown by Evans and Ferreira (2011) that PG(M3) ≇PG(M4).We show that M3 has a reduct Mclq such that PG(M4) ≅PG(Mclq). To achieve this we show that Mclq is a slightly generalised Fraisse-Hrushovski limit incorporating non-eliminable imaginary sorts in Mclq.

Original languageEnglish
Pages (from-to)151-164
Number of pages14
JournalFundamenta Mathematicae
Volume247
Issue number2
DOIs
StatePublished - 1 Jan 2019

Keywords

  • Hrushovski construction
  • Predimension

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