论文标题
可计数均匀的Steiner三重系统避免了指定子系统
Countable homogeneous Steiner triple systems avoiding specified subsystems
论文作者
论文摘要
In this article we construct uncountably many new homogeneous locally finite Steiner triple systems of countably infinite order as Fra\"ıssé limits of classes of finite Steiner triple systems avoiding certain subsystems. The construction relies on a new embedding result: any finite partial Steiner triple system has an embedding into a finite Steiner triple system that contains no nontrivial proper subsystems that are not subsystems of原始的部分系统。
In this article we construct uncountably many new homogeneous locally finite Steiner triple systems of countably infinite order as Fra\"ıssé limits of classes of finite Steiner triple systems avoiding certain subsystems. The construction relies on a new embedding result: any finite partial Steiner triple system has an embedding into a finite Steiner triple system that contains no nontrivial proper subsystems that are not subsystems of the original partial system. Fra\"ıssé's construction and its variants are rich sources of examples that are central to model-theoretic classification theory, and recently infinite Steiner systems obtained via Fra\"ıssé-type constructions have received attention from the model theory community.
