Reducts of Hrushovski’s constructions of a higher geometrical arity

Assaf Hasson, Omer Mermelstein Fundamenta Mathematicae MSC: Primary 03C30, 03C45; Secondary 03C13. DOI: 10.4064/fm645-10-2018 Opublikowany online: 31 May 2019

Streszczenie

Let $\mathbb {M}_n$ denote the structure obtained from Hrushovski’s (non-collapsed) construction with an $n$-ary relation and $\operatorname{PG} (\mathbb {M}_n)$ its associated pregeometry. It was shown by Evans and Ferreira (2011) that $\operatorname{PG} (\mathbb {M}_3)\not \cong \operatorname{PG} (\mathbb {M}_4)$. We show that $\mathbb {M}_3$ has a reduct $\mathbb {M}^{\operatorname{clq} }$ such that $\operatorname{PG} (\mathbb {M}_4)\cong \operatorname{PG} (\mathbb {M}^{\operatorname{clq} })$. To achieve this we show that $\mathbb {M}^{\operatorname{clq} }$ is a slightly generalised Fraïssé–Hrushovski limit incorporating non-eliminable imaginary sorts in $\mathbb {M}^{\operatorname{clq} }$.

Autorzy

  • Assaf HassonDepartment of Mathematics
    Ben Gurion University of the Negev
    P.O.B. 653, Be’er Sheva 8410501, Israel
    e-mail
  • Omer MermelsteinDepartment of Mathematics
    Ben Gurion University of the Negev
    P.O.B 653, Be’er Sheva 8410501, Israel
    e-mail

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