Martin Goldstern 
Wed, 24 Aug 2005 

Structure and nonstructure in the clone lattice 

A "clone" on a set X is a set of finitary operations
on X which is closed under composition and contains 
all projections (equivalently: the set of term 
functions of some universal algebra on X). 

The set of all clones on X forms a complete lattice. 
We investigate naturally appearing subsets of
this lattice (such as: the set of atoms, intervals
between interesting elements, etc); few are well
understood, many are known to be very complicated. 

I will describe a few results, and present open problems.