Large intervals in the clone lattice

We give three examples of cofinal intervals in the lattice of (local) clones on an infinite set X, whose structure is on the one hand non-trivial but on the other hand reasonably well understood. Specifically, we will exhibit clones l₁, l₂, l₃ such that (1) the interval [l₁,]in the lattice of local clones is (as a lattice) isomorphic to {0, 1, 2, ...} under the divisibility relation,(2)the interval in the lattice of local clones is isomorphic to the congruence lattice of an arbitrary semilattice, (3) in the lattice of all clones is isomorphic to the lattice of all filters on X.