Abstract In this paper, we make some considerations about admissible orders on the set of closed subintervals of the unit interval I [ 0 , 1 ] , i.e. linear orders that refine the product order on intervals. We propose a new way to generate admissible orders on I [ 0 , 1 ] which is more general than those we find in the current literature. Also, we deal with the possibility of an admissible order on I [ 0 , 1 ] to be isomorphic to the usual order on [ 0 , 1 ] . We prove that some orders constructed by our method are not isomorphic to the usual one and we make some considerations about the following question: is there some admissible order on I [ 0 , 1 ] isomorphic to the usual order on [ 0 , 1 ] ?

中文翻译：

---

在 [0,1] 的封闭子区间上的可接受订单

摘要 在本文中，我们考虑了单位区间I [ 0 , 1 ] 的闭子区间集上的可容许阶数，即在区间上细化乘积阶数的线性阶数。我们提出了一种在 I [ 0 , 1 ] 上生成可接受阶数的新方法，它比我们在当前文献中发现的更通用。此外，我们处理了在 I [ 0 , 1 ] 上的可接受顺序与 [ 0 , 1 ] 上的通常顺序同构的可能性。我们证明了我们的方法构造的一些阶与通常的阶不同构，我们对以下问题进行了一些考虑：I [ 0 , 1 ] 上是否有一些与 [ 0 , 1 ] 上的通常阶同构的可接受阶？