论文标题
通用平坦的先例
The generic flat pregeometry
论文作者
论文摘要
我们检查了通过Hrushovski构造构建的结构的一阶结构。特别是，我们表明，平坦的先例类别是合并类别，因此无界的Arity hrushovski结构的预制恰好是其通用的。我们表明，通用性是饱和的，为其理论提供了公理化，表明该理论是$ω$稳定的，并且具有量词 - 淘汰量为$ \ forall $ -formulas的布尔组合。我们表明，有界的hrushovski构造的预言满足了相同的理论，并且实际上它们形成了基本链。
We examine the first order structure of pregeometries of structures built via Hrushovski constructions. In particular, we show that the class of flat pregeometries is an amalgamation class such that the pregeometry of the unbounded arity Hrushovski construction is precisely its generic. We show that the generic is saturated, provide an axiomatization for its theory, show that the theory is $ω$-stable, and has quantifier-elimination down to boolean combinations of $\exists\forall$-formulas. We show that the pregeometries of the bounded-arity Hrushovski constructions satisfy the same theory, and that they in fact form an elementary chain.
