Publication Date: 2020
Notre Dame Journal of Formal Logic (00294527)61(1)pp. 1-10
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. © 2020 by University of Notre Dame
Publication Date: 2019
Bulletin Of The Iranian Mathematical Society (10186301)45(6)pp. 1839-1854
We show that the Hrushovski–Fraïssé limit of certain classes of trees lead to strictly superstable theories of various U-ranks. In fact, for each α∈ ω+ 1 \ { 0 } we introduce a strictly superstable theory of U-rank α. Furthermore, we show that these theories are decidable and pseudofinite. © 2019, Iranian Mathematical Society.
