论文标题
等级公理和超图
Rank axioms and supersimplicity
论文作者
论文摘要
正如Lascar的抽象等级概念Axiomatize Axiomatize u-Rank一样，我们为排名$ su^d $和$ su^f $的公理提出了公理，这是分裂和分叉的基础等级。我们研究这些公理之间的关系。与Superstable一样，我们根据这些等级的存在来表征Supersimple类型和理论。我们表明，U级是拉斯卡分裂独立关系的基础等级。我们还提供了类似于U的原始定义的SUD的替代定义。最后，我们检查，如果在简单和超级简单的标准特征中，我们改变了非拉斯卡分裂独立性的非架子独立性，我们会表征稳定且超级超凡的。
Just as Lascar's notion of abstract rank axiomatizes the U-rank, we propose axioms for the ranks $SU^d$ and $SU^f$, the foundation ranks of dividing and forking. We study the relationships between these axioms. As with superstable, we characterize supersimple types and theories based on the existence of these ranks. We show that the U-rank is the foundation rank of the Lascar-splitting independence relationship. We also provide an alternative definition of SUd similar to the original definition of U. Finally, we check that if in the standard characterizations of simple and supersimple we change the non-forking independence for the non-lascar-splitting independence, we characterize stable and superstable.
