The cube problem for linear orders
Garrett Ervin: University of California - Irvine
Location: Hill 705
Date & time: Monday, 20 March 2017 at 5:00PM - 5:11PM
In the 1950s, Sierpinski asked whether there exists a linear order that is isomorphic to its lexicographically ordered cartesian cube but not to its square. The analogous question has been answered positively for many different classes of structures, including groups, Boolean algebras, topological spaces, graphs, partial orders, and Banach spaces. However, the answer to Sierpinskiâ€™s question turns out to be negative: any linear order that is isomorphic to its cube is already isomorphic to its square, and thus to all of its finite powers. I will present an outline of the proof and give some related results.