The number of finitely generated infinite cylindric set algebras of dimension two

There are exactly seven isomorphism types of infinite one-generated diagonal-free cylindric set algebras of dimension two all of which are described in this paper. Contrast this result with the following facts from another paper by the same author: there are continuum many two-generated such algebras and continuum many one-generated ones of finite dimension at least three.Presented by J. Mycielski.