Order polynomially complete lattices must be LARGE
逻辑
2016-09-07 v1
摘要
If L is an order polynomially complete lattice, (that is: every monotone function from L^n to L is induced by a lattice-theoretic polynomial) then the cardinality of L is a strongly inaccessible cardinal. In particular, the existence of such lattices is not provable in ZFC, nor from ZFC+GCH. Although the problem originates in algebra, the proof is purely set-theoretical. The main tools are partition and canonisation theorems. It is still open if the existence of infinite o.p.c. lattices can be refuted in ZFC.
引用
@article{arxiv.math/9707203,
title = {Order polynomially complete lattices must be LARGE},
author = {Martin Goldstern and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9707203},
year = {2016}
}
备注
This is paper number GoSh:633 in Shelah's list. The paper is to appear in Algebra Universalis.