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January 2020 Pseudofiniteness in Hrushovski Constructions
Ali N. Valizadeh, Massoud Pourmahdian
Notre Dame J. Formal Logic 61(1): 1-10 (January 2020). DOI: 10.1215/00294527-2019-0038

Abstract

In a relational language consisting of a single relation R, we investigate pseudofiniteness of certain Hrushovski constructions obtained via predimension functions. It is notable that the arity of the relation R plays a crucial role in this context. When R is ternary, by extending the methods recently developed by Brody and Laskowski, we interpret Q+,< in the K+,-generic and prove that this structure is not pseudofinite. This provides a negative answer to the question posed in an earlier work by Evans and Wong. This result, in fact, unfolds another aspect of complexity of this structure, along with undecidability and the strict order property proved in the mentioned earlier works. On the other hand, when R is binary, it can be shown that the K+,-generic is decidable and pseudofinite.

Citation

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Ali N. Valizadeh. Massoud Pourmahdian. "Pseudofiniteness in Hrushovski Constructions." Notre Dame J. Formal Logic 61 (1) 1 - 10, January 2020. https://doi.org/10.1215/00294527-2019-0038

Information

Received: 5 May 2018; Accepted: 27 September 2018; Published: January 2020
First available in Project Euclid: 29 November 2019

zbMATH: 07196089
MathSciNet: MR4054242
Digital Object Identifier: 10.1215/00294527-2019-0038

Subjects:
Primary: 03C99
Secondary: 05C05 , 05C63 , 05C65

Keywords: Ehrenfeucht–Fraïssé games , generic structures , Hrushovski constructions , predimension , pseudofinite structures

Rights: Copyright © 2020 University of Notre Dame

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Vol.61 • No. 1 • January 2020
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