AI 中文总结
该研究在选择公理下，通过直接证明序论树类被树同态关系良拟序，恢复了Nash-Williams无限树定理的弱化版本且避免使用更好拟序。
AI 中文摘要
在选择公理成立的前提下，我们证明可恢复Nash-Williams关于无限树定理的弱化版本，同时完全避免使用更好拟序；特别地，我们直接证明所有序论树构成的类被树同态关系良拟序。
英文摘要
We introduce an ordinal-valued invariant of well-founded trees, called their type. We use type to give an alternative proof that the class of all well-founded trees is well-quasi-ordered by the homomorphism relation, and we establish a relationship between type and the usual ordinal rank of a well-founded tree, showing in particular that type provides a strictly coarser structural classification.
Comments9 pages; I did not know about rank when I wrote the previous version, hence the change of title and abstract
