论文标题
自由结构和限制密度
Free structures and limiting density
论文作者
论文摘要
格罗莫夫（Gromov）问一个典型（有限的）群体是什么样的，他提出了一种方法，以使问题在限制密度方面进行精确。已知典型的有限生成的组可与非亚伯自由组共享一些重要的属性。我们更普遍地问格罗莫夫的问题，以任意代数品种的结构（在普遍代数的意义上），并带有特定形式的介绍。我们专注于基本特性。我们举例说明了限制密度的不同行为。基于示例，我们确定了自由结构的基本一阶理论的足够条件，以匹配典型结构的结构。即，在自由结构中，句子是限制密度1。
Gromov asked what a typical (finitely presented) group looks like, and he suggested a way to make the question precise in terms of limiting density. The typical finitely generated group is known to share some important properties with the non-abelian free groups. We ask Gromov's question more generally, for structures in an arbitrary algebraic variety (in the sense of universal algebra), with presentations of a specific form. We focus on elementary properties. We give examples illustrating different behaviors of the limiting density. Based on the examples, we identify sufficient conditions for the elementary first-order theory of the free structure to match that of the typical structure; i.e., a sentence is true in the free structure iff it has limiting density 1.
