For reference, "Cantor complete" means that every nested sequence of bounded closed intervals has non-empty intersection.
It is easy to show that the conditions "Cauchy complete" and "Cantor complete" are equivalent in Archimedean ordered fields. However in terms of non-Archimedean fields, I think those two completeness shouldn’t be equivalent.
In this paper, https://arxiv.org/pdf/1101.5652 ,in theorem 6.6,Cantor k-complete(or Cantor complete) implies Cauchy complete and it’s not a sufficient and necessary condition.
It should be noticed that all the Cauchy complete examples given from that paper and this link Example of a complete, non-archimedean ordered field, are Cantor complete or Spherical complete, like the Hahn series field, Laurent series field and Robinson’s Asymptotic field.
So, can anyone give some examples that only satisfying Cauchy complete but not Cantor complete, or just prove that those two completeness are equivalent in the non-Archimedean case. I would be most grateful for your kind response.
