Finitely generated pseudosimple algebras

We prove that there exist finitely generated algebras, which are pseudosimple but not simple. This problem goes back to Henkin, Monk, Tarski 71]. In fact, for any limit ordinal i, there exists a pseudosimple algebra, which has no proper subalgebra and whose congruence lattice is ⁱ+1. (Here ⁱ denotes ordinal power).Presented by George Grätzer.Research supported by Hungarian National Foundation for Scientific Research grant No. 1810.