In mathematics, a Cantor algebra, named after Georg Cantor, is one of two closely related Boolean algebras, one countable and one complete.
This is the free Boolean algebra on a countable number of generators.
Up to isomorphism, this is the only nontrivial Boolean algebra that is both countable and atomless.
The complete Cantor algebra is the complete Boolean algebra of Borel subsets of the reals modulo meager sets (Balcar & Jech 2006).
The complete Cantor algebra was studied by von Neumann in 1935 (later published as (von Neumann 1998)), who showed that it is not isomorphic to the random algebra of Borel subsets modulo measure zero sets.