  We investigate the structure of the lattice of clones on an infinite set X.
We first observe that ultrafilters naturally induce clones; this yields a
simple proof of Rosenberg's theorem:
  "there are 2^2^kappa many maximal (=precomplete) clones on a set of size
kappa." The clones we construct here do not contain all unary functions.
  We then investigate clones that do contain all unary functions. Using a
strong negative partition theorem we show that for many cardinals kappa there
are 2^2^kappa many such clones on a set of size kappa.
  Finally, we show that on a weakly compact cardinal there are exactly 2
maximal clones which contain all unary functions.
