论文标题
Aronszajn线的分解定理
A Decomposition Theorem for Aronszajn Lines
论文作者
论文摘要
我们表明，在适当的迫使Axiom下，所有Aronszajn线的类的行为就像$σ$ scedder的订单在嵌入性关系下。特别是，我们能够证明，标记为零散的Aronszajn线的一类更好的准级线本身就是一个更好的准顺序。此外，我们表明，标有Aronszajn线的每个更好的准订单可以表示为有限的标记类型的总和，这些类型在代数上是不可分解的。通过用有限标记的树编码线条，我们还可以推断出分解结果，对于每条Aronszajn行$ l $，都有整数n，因此，对于任何有限的颜色$ l $，都有$ l^\ prime l^prime of $ l $ l $ iSomorphic to $ l $ to $ l $不再使用n颜色。
We show that under the proper forcing axiom the class of all Aronszajn lines behave like $σ$-scattered orders under the embeddability relation. In particular, we are able to show that the class of better quasi order labeled fragmented Aronszajn lines is itself a better quasi order. Moreover, we show that every better quasi order labeled Aronszajn line can be expressed as a finite sum of labeled types which are algebraically indecomposable. By encoding lines with finite labeled trees, we are also able to deduce a decomposition result, that for every Aronszajn line $L$ there is integer n such that for any finite colouring of $L$ there is subset $L^\prime$ of $L$ isomorphic to $L$ which uses no more than n colours.
