**
Congruence lattices of lattices**

The
"Congruence Lattice Problem" in the Wikipedia
**
**

**Open
problems**

**Problem 1.
**Does there
exists a distributive algebraic lattice which is not isomorphic to the
congruence lattice of any algebraic structure with only finitely many operations ?
What lattices are congruence lattices of algebras with only finitely many
operations?

**Problem 2. **
( Lampe)** ** Is there an algebra *A* with exactly
**
א _{i}**

**Problem 3.
**Is every finite distributive lattice isomorphic to the congruence lattice of
an isoform modular lattice ?

**Problem 4.
**(Lampe) Which algebraic lattices are isomorphic to the congruence lattices
of algebras having one element subalgebras ?