  An FN lattice $F$ is a simple, infinite, semidistributive lattice. Its
existence was recently proved by R. Freese and J.\,B. Nation. Let
$\mathsf{B}_n$ denote the Boolean lattice with $n$ atoms. For a lattice $K$,
let $K^+$ denote $K$ with a new unit adjoined.
  We prove that the finite distributive lattices: $\mathsf{B}_0^+,
\mathsf{B}_1^+,\mathsf{B}_2^+, \dots$ can be represented as congruence lattices
of infinite semidistributive lattices. The case $n = 0$ is the Freese-Nation
result, which is utilized in the proof.
  We also prove some related representation theorems.

Rings and Algebras