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Wednesday, January 30, 2019

**Abstract:** We sketch proofs of solutions to two old problems posed by Sierpinski concerning products of linear orders. The first problem asks whether there exists a linear order $X$ that is isomorphic to its lexicographic cube but not to its square; the second, whether there are two non-isomorphic orders $Y$ and $Z$ that divide each other on both the left and right side. For other classes of structures, the corresponding questions are usually either both positive or both negative, but for linear orders the answers diverge: there is no such $X$, but there are such $Y$ and $Z$.

Wednesday, February 6, 2019

Friday, February 8, 2019

Wednesday, February 13, 2019

Friday, February 15, 2019

Monday, February 18, 2019

Friday, February 22, 2019

Friday, March 1, 2019