# Sh:688

- Goldstern, M., & Shelah, S. (1999).
*There are no infinite order polynomially complete lattices, after all*. Algebra Universalis,**42**(1-2), 49–57. arXiv: math/9810050 DOI: 10.1007/s000120050122 MR: 1736340 -
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.

- 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}, doi = {10.1007/s000120050122}, mrclass = {03E25 (03E55 06A07 08A40)}, mrnumber = {1736340}, mrreviewer = {Yehuda Rav}, doi = {10.1007/s000120050122}, note = {\href{https://arxiv.org/abs/math/9810050}{arXiv: math/9810050}}, arxiv_number = {math/9810050} }