论文标题
抽象小学类中的简单独立关系
Simple-like independence relations in abstract elementary classes
论文作者
论文摘要
我们在具有怪物模型的AEC背景下介绍和研究简单而超级独立的关系。 $定理$：让$ k $是具有怪物模型的AEC。 - 如果$ k $具有简单的独立关系，则$ k $没有2树的属性。 - 如果$ k $具有$（<\ aleph_0）$的简单独立关系 - 证人属性，则$ k $没有树属性。 这两个事实的证明是通过在固定模型上找到与大型子集不一致的固定模型的小型Galois类型类别来完成的。我们认为，这种计数类型的方法本身就是一个有趣的概念。我们通过在独立关系的地方假设下的Lascar等级的有限性来表征超级独立关系。
We introduce and study simple and supersimple independence relations in the context of AECs with a monster model. $Theorem$: Let $K$ be an AEC with a monster model. - If $K$ has a simple independence relation, then $K$ does not have the 2-tree property. - If $K$ has a simple independence relation with $(<\aleph_0)$-witness property, then $K$ does not have the tree property. The proof of both facts is done by finding cardinal bounds to classes of small Galois-types over a fixed model that are inconsistent for large subsets. We think this finer way of counting types is an interesting notion in itself. We characterize supersimple independence relations by finiteness of the Lascar rank under locality assumptions on the independence relation.
