Aronszajn线的一个分解定理
A Decomposition Theorem for Aronszajn Lines
摘要：
我们表明，适当的强制公理下的类的所有Aronszajn线的行为像$σ$ -分散订单下的嵌入关系。特别是，我们能够证明，一类更好的准序标记的片段Aronszajn线本身是一个更好的准序。此外，我们证明了每一个更好的准序标记Aronszajn线可以表示为一个有限的代数不可分解的标记类型的和。通过用有限标记树编码线，我们还能够推导出分解结果，即对于每个Aronszajn线$L$，存在整数n，使得对于$L$的任何有限着色，存在与$L$同构的$L$的子集$L^\prime$，其使用不超过n种颜色。
英文摘要：
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.
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