Pruning of intervals

(you need flash player for Fig. 2)

We call a lattice *L* **isoform**, if
for any congruence relation θ of *L*, all congruence classes of θ
are isomorphic sublattices.

We have proved that for every finite distributive lattice *D*,
there exists a finite, isoform lattice *L* such that the
congruence

lattice of *L* is isomorphic to *D* ( ** G. Grätzer
and E. T. Schmidt**, *Finite lattices with isoform
congruences * (pdf) ).

New result (2003):
**G. Grätzer , R. W. Quackenbush and E. T. Schmidt**, *Congruence-
preserving extensions
of finite lattices to isoform lattices.* (pdf) .We have proved:

Here is an example. Take the lattice *K *given on
Figure 1:

We have an embedding into a cubic extension (this
is a direct product) and prune (delete)
an edge to get the lattice *L, *

see* *on Figure 2 the blinking edge: