发表机构
University of Maryland（马里兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在一元NIP理论中证明不变全局类型的强分解定理，并由此得出分叉的逐坐标判据及可定义类型的稠密性。
AI 中文摘要
我们在一元NIP理论中获得了不变全局类型的强分解定理。由此，我们证明：若一个n型tp(ā/MC)在M上不分叉，则ā=(f̄,d̄)，其中tp(d̄/MC)是M可定义的，且tp(f̄/MCd̄)在M中有限满足。对于任意基集B，我们证明：一个n型tp(ā/BC)在B上不分叉当且仅当对每个单元素a_i∈ā，tp(a_i/BC)在B上不分叉。我们证明一元NIP理论满足可定义类型在非分叉扩张中的稠密性。
英文摘要
We obtain a strong decomposition theorem for invariant global types in a monadically NIP theory. From this, we prove that if an $n$-type $tp(\bar{a}/MC)$ does not fork over $M$ then $\bar{a}=(\bar{f},\bar{d})$ where $tp(\bar{d}/MC)$ is $M$-definable and $tp(\bar{f}/MC\bar{d})$ is finitely satisfied in $M$. Over arbitrary base sets $B$, we prove that an $n$-type $tp(\bar{a}/BC)$ does not fork over $B$ if and only if $tp(a_i/BC)$ does not fork over $B$ for each singleton $a_i\in\bar{a}$. We show that monadically NIP theories satisfy density of definable types among non-forking extensions.
