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

2016/09/26 by Garrett Ervin, Ervin, Garrett · 1 citation
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.1609.07872

arxiv created 2016/09/26 · arxiv updated 2016/09/27

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 Xⁿ, n>1, it is isomorphic to all of them.

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• Algebraic structures arising from the finite condensation on linear orders

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