单子NIP理论中的分叉
Forking in monadically NIP theories
AI总结：
本文证明单子NIP理论中分叉在任意集合上满足强平凡性，推广了Baldwin-Shelah结果，并给出无有限扩展基的ω-范畴例子。
AI中文摘要：
我们证明，在单子NIP理论中，分叉在任意集合上满足一种非常强的平凡性形式，这推广了单子稳定理论中的Baldwin-Shelah结果，并类似于Shelah在单子NIP理论中关于模型上有限可满足性的结果。这尤其意味着严格非分叉独立性具有特别良好的性质，并且分叉关系在单元素上诱导出一个典范的半线性偏序。我们还给出了一个ω-范畴的单子NIP理论的例子，使得没有有限集是扩展基。
英文摘要：
We demonstrate that forking in monadically NIP theories satisfies a very strong form of triviality over arbitrary sets, generalizing Baldwin-Shelah in monadically stable theories and analogous to Shelah's result for finite satisfiability over models in monadically NIP theories. This implies in particular that strict non-forking independence is particularly well behaved, and that the forking relation induces a canonical semilinear partial order on singletons. We also give an example of an $ω$-categorical monadically NIP theory so that no finite set is an extension base.
