阶多项式完全格必须是LARGE
Order polynomially complete lattices must be LARGE
摘要：
如果L是一个阶多项式完全格，（即：从L^n到L的每个单调函数都是由一个格论多项式诱导的）则L的基数是一个强不可达基数。特别地，这种格的存在性在ZFC中是不可证明的，也不能从ZFC+GCH中证明。虽然这个问题起源于代数，但证明是纯集合论的。主要的工具是划分和经典化定理。它仍然是开放的，如果存在无限的o.p.c.格可以在ZFC中被反驳。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
