Some Remarks on Generic Structures

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Journal of Symbolic Logic 74 (4):1143-1154 (2009)
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Abstract

We show that the N₀-categorical structures produced by Hrushovski's predimension construction with a control function fit neatly into Shelah's $SOP_n $ hierarchy: if they are not simple, then they have SOP₃ and NSOP₄. We also show that structures produced without using a control function can be undecidable and have SOP.

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10.2178/jsl/1254748684

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Citations of this work

Pseudofiniteness in Hrushovski Constructions.Ali N. Valizadeh & Massoud Pourmahdian - 2020 - Notre Dame Journal of Formal Logic 61 (1):1-10.

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References found in this work

A new strongly minimal set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
[Introduction].Wilfrid Hodges - 1988 - Journal of Symbolic Logic 53 (1):1.
Toward classifying unstable theories.Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (3):229-255.
On generic structures.D. W. Kueker & M. C. Laskowski - 1992 - Notre Dame Journal of Formal Logic 33 (2):175-183.
ℵ0-categorical structures with a predimension.David M. Evans - 2002 - Annals of Pure and Applied Logic 116 (1-3):157-186.

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