### There are no infinite order polynomially complete lattices, after all

by Goldstern and Shelah. [GoSh:688]

Algebra Universalis, 1999

If L is a lattice with the interpolation property
whose cardinality is a strong limit cardinal of uncountable
cofinality, then some finite power L^n has an antichain of
size~ kappa . Hence there are no infinite opc lattices
(i.e., lattices on which every n-ary monotone function is a
polynomial).
However, the existence of strongly
amorphous sets implies (in ZF) the existence of infinite opc
lattices.

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