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.

Back to the list of publications