论文标题
布尔类型在依赖理论中
Boolean Types in Dependent Theories
论文作者
论文摘要
可以自然而然地将完整类型的概念推广，以允许将任意布尔代数B中的值分配给每个公式。我们展示了有关B的性质对此类类型行为的影响的一些基本结果，并表明它们在NIP理论的情况下表现得很好。特别是，我们概括了第三作者对计数类型的结果，以及平滑类型的概念，并将类型扩展到平滑类型。然后，我们证明Keisler度量与某些布尔类型相关，并表明可以将某些结果转移到措施中 - 特别是，提供了一个替代证明，即相关理论中的每个度量都可以扩展到平滑的理论中。我们还研究了稳定的情况。我们认为本文是对布尔类型主题进行更多研究的邀请。
The notion of a complete type can be generalized in a natural manner to allow assigning a value in an arbitrary Boolean algebra B to each formula. We show some basic results regarding the effect of the properties of B on the behavior of such types, and show they are particularity well behaved in the case of NIP theories. In particular, we generalize the third author's result about counting types, as well as the notion of a smooth type and extending a type to a smooth one. We then show that Keisler measures are tied to certain Boolean types and show that some of the results can thus be transferred to measures - in particular, giving an alternative proof of the fact that every measure in a dependent theory can be extended to a smooth one. We also study the stable case. We consider this paper as an invitation for more research into the topic of Boolean types.
