Every linear order isomorphic to its cube is isomorphic to its square

Garrett Ervin

paper

Every linear order isomorphic to its cube is isomorphic to its square

arXiv:1609.07872

Abstract

In 1958, Sierpinski asked whether there exists a linear order $X$ 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 $X$ is isomorphic to any one of its finite powers $X^{n}$ , $n > 1$ , it is isomorphic to all of them.