Reducts of Hrushovski's constructions of a higher geometrical arity

Assaf Hasson; Omer Mermelstein

doi:10.4064/fm645-10-2018

Reducts of Hrushovski's constructions of a higher geometrical arity

Assaf Hasson, Omer Mermelstein

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

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 M^clq such that PG(M₄) ≅PG(M^clq). To achieve this we show that M^clqis a slightly generalised Fraisse-Hrushovski limit incorporating non-eliminable imaginary sorts in M^clq.

Original language	American English
Pages (from-to)	151-164
Number of pages	14
Journal	Fundamenta Mathematicae
Volume	247
Issue number	2
DOIs	https://doi.org/10.4064/fm645-10-2018
State	Published - 31 May 2019

Keywords

Hrushovski construction
Predimension

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.4064/fm645-10-2018

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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.",

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N2 - 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.

AB - 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.

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KW - Predimension

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Reducts of Hrushovski's constructions of a higher geometrical arity

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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