Souslin代数嵌入
Souslin Algebra Embeddings
摘要：
一个Souslin代数是一个完全布尔代数，其主要特征是由一个反链条件与一个无限分配律的紧密结合所决定的。本文分为两个部分。第一部分建立了Souslin代数的完备无原子子代数的表示论（建立在Jech和Jensen的思想上）。由此得到了关于子代数的可能类型及其相互关系的一些基本结果。第二部分首先回顾了描述集合论关于Baire范畴的一些推广结果，然后将这些结果用于非平凡Souslin树的构造，得到了具有显著子代数结构的Souslin代数。特别地，我们用这种方法证明，在钻石原则下，有一个双嵌入，但不是同构的齐次Souslin代数对。
英文摘要：
A Souslin algebra is a complete Boolean algebra whose main features are ruled by a tight combination of an antichain condition with an infinite distributive law. The present article divides into two parts. In the first part a representation theory for the complete and atomless subalgebras of Souslin algebras is established (building on ideas of Jech and Jensen). With this we obtain some basic results on the possible types of subalgebras and their interrelation. The second part begins with a review of some generalizations of results from descriptive set theory concerning Baire category which are then used in non-trivial Souslin tree constructions that yield Souslin algebras with a remarkable subalgebra structure. In particular, we use this method to prove that under the diamond principle there is a bi-embeddable though not isomorphic pair of homogeneous Souslin algebras.
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