Every linear order isomorphic to its cube is isomorphic to its square
Logic
2016-09-28 v1
Abstract
In 1958, Sierpinski asked whether there exists a linear order that is isomorphic to its lexicographically ordered cube but is not isomorphic to its square. The main result of this paper is that the answer is negative. More generally, if is isomorphic to any one of its finite powers , , it is isomorphic to all of them.
Cite
@article{arxiv.1609.07872,
title = {Every linear order isomorphic to its cube is isomorphic to its square},
author = {Garrett Ervin},
journal= {arXiv preprint arXiv:1609.07872},
year = {2016}
}