# Sh:688

• Goldstern, M., & Shelah, S. (1999). There are no infinite order polynomially complete lattices, after all. Algebra Universalis, 42(1-2), 49–57.
• Abstract:
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.

• Version 1999-08-31_11 (8p) published version (9p)
Bib entry
@article{Sh:688,
author = {Goldstern, Martin and Shelah, Saharon},
title = {{There are no infinite order polynomially complete lattices, after all}},
journal = {Algebra Universalis},
fjournal = {Algebra Universalis},
volume = {42},
number = {1-2},
year = {1999},
pages = {49--57},
issn = {0002-5240},
mrnumber = {1736340},
mrclass = {03E25 (03E55 06A07 08A40)},
doi = {10.1007/s000120050122},
note = {\href{https://arxiv.org/abs/math/9810050}{arXiv: math/9810050}},
arxiv_number = {math/9810050}
}