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Preprint Number 1516

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1516. Ali Valizadeh and Massoud Pourmahdian
Pseudofiniteness in Hrushovski Constructions

Submission date: 12 November 2018


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 developed in [BL12], we interpret < ℚ^+ , < > in the < K^+_0, ≤^* >-generic and prove that this structure is not pseudofinite. This provides a negative answer to the question posed in [EW09] (Question 2.6). This result, in fact, unfolds another aspect of complexity of this structure, along with undecidability and strict order property proved in [EW09] and [Bl12]. On the other hand, when R is binary, it can be shown that the < K^+_0, ≤^* >-generic is decidable and pseudofinite.

Mathematics Subject Classification: 03C45, 03C50, 03C20

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Full text arXiv 1811.04692: pdf, ps.

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