T \subseteq ds（α）上的一致n位函数
Uniform n-place functions on T\subseteq ds(α)
摘要：
本文将Erdos-Rado定理推广到良基树类。我们定义了类rs（infty）^{< aleph_0}（序数递减序列的有限序列）与aleph_0等价类的等价关系，并对n< omega定义了rs（infty）^{< aleph_0}的mu色着色的n端一致性概念.然后我们证明了对于每个序数alpha，n< omega和基数mu，存在一个序数lambda，使得对于T=rs（lambda）^{< aleph_0}的任何带有mu颜色的着色c，T包含与rs（alpha）同构的S，使得c rest S^{< aleph_0}是n端一致的。对于定义域T^n的c，这等价于找到同构于rs（alpha）的S子集T，使得c upharpoonright S^{n}仅依赖于所定义关系的等价类，因此特别是T->（rs（alpha））^ n_{mu, aleph_0}。我们还得出了一个结论，着色的n-元组从一个分散的线性秩序。
英文摘要：
In this paper the Erdos-Rado theorem is generalized to the class of well founded trees. We define an equivalence relation on the class rs(infty)^{< aleph_0} (finite sequences of decreasing sequences of ordinals) with aleph_0 equivalence classes, and for n< omega a notion of n-end-uniformity for a colouring of rs(infty)^{< aleph_0} with mu colours. We then show that for every ordinal alpha, n< omega and cardinal mu there is an ordinal lambda so that for any colouring c of T=rs(lambda)^{< aleph_0} with mu colours, T contains S isomorphic to rs(alpha) so that c rest S^{< aleph_0} is n-end uniform. For c with domain T^n this is equivalent to finding S subseteq T isomorphic to rs(alpha) so that c upharpoonright S^{n} depends only on the equivalence class of the defined relation, so in particular T-> (rs(alpha))^n_{mu, aleph_0} . We also draw a conclusion on colourings of n-tuples from a scattered linear order.
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