论文标题
拉姆西学位：大诉小
Ramsey degrees: big v. small
论文作者
论文摘要
在本文中，我们研究了满足某些轻度条件的类别中大拉姆西学位的代数特性。作为概括的第一个非平地后果，我们在本文中提倡，我们证明了小的拉姆西学位是相应大的大型的最小值。我们还证明，大拉姆西学位是亚基的，表明平等是通过我们称为自相似性的对象的抽象属性来实现的。最后，我们应用了本文开发的抽象机制，以表明，如果可数的关系结构具有有限的大拉姆西学位，那么它的无量词还原也是如此。特别是，因此，（q，<），随机图，随机锦标赛和（q，<，0）的还原都具有有限的大拉姆西学位。
In this paper we investigate algebraic properties of big Ramsey degrees in categories satisfying some mild conditions. As the first nontrivial consequence of the generalization we advocate in this paper we prove that small Ramsey degrees are the minima of the corresponding big ones. We also prove that big Ramsey degrees are subadditive and show that equality is enforced by an abstract property of objects we refer to as self-similarity. Finally, we apply the abstract machinery developed in the paper to show that if a countable relational structure has finite big Ramsey degrees, then so do its quantifier-free reducts. In particular, it follows that the reducts of (Q, <), the random graph, the random tournament and (Q, <, 0) all have finite big Ramsey degrees.
