论文标题
从拉姆西学位到拉姆西的扩展
From Ramsey degrees to Ramsey expansions via weak amalgamation
论文作者
论文摘要
在没有其他假设的情况下，在本文中，我们为具有有限的小拉姆西学位的每类有限对象构建了一个拉姆齐的扩展。我们的构建是基于小的拉姆西学位，薄弱的合并和有关弱的Fraïssé类别的结果之间的关系。也就是说，概括每个拉姆齐级都有合并的事实，我们表明有有限的拉姆西学位的课程较弱。然后，我们调用弱Fraïssé类别的机械来执行构造。这改善了以前的类似结果，在假设一切都舒适地坐落在具有足够的基础设施的较大阶级的假设下进行类似的结构，并且在这种更广泛的背景下，有一个超双重结构的结构。
Under no additional assumptions, in this paper we construct a Ramsey expansion for every category of finite objects with finite small Ramsey degrees. Our construction is based on the relationship between small Ramsey degrees, weak amalgamation and recent results about weak Fraïssé categories. Namely, generalizing the fact that every Ramsey class has amalgamation, we show that classes with finite Ramsey degrees have weak amalgamation. We then invoke the machinery of weak Fraïssé categories to perform the construction. This improves previous similar results where an analogous construction was carried out under the assumption that everything sits comfortably in a bigger class with enough infrastructure, and that in this wider context there is an ultrahomogeneous structure under whose umbrella the construction takes place.
