毕竟不存在无限阶多项式完全格
There are no infinite order polynomially complete lattices after all
摘要：
一个格L称为opc，如果每个单调函数f：L^n -> L由一个多项式诱导.我们在这里展示：如果L是一个具有插值性质的格，其基数是一个不可数共尾性的强极限基数，则某个有限幂L^n有一个大小为kappa的反链。使用我们之前的结果（xxx存档中的math.LO/9707203），即无限opc格的基数必须是不可访问的，我们现在可以得出结论，不存在无限opc格。然而，强无定形集的存在意味着（在ZF中）无限opc格的存在。
英文摘要：
A lattice L is called opc if every monotone function f : L^n -> L is induced by a polynomial. We show here: 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. Using our previous result (math.LO/9707203 in the xxx archive) that the cardinality of an infinite opc lattice must be inaccessible, we can now conclude that there are no infinite opc lattices. However, the existence of strongly amorphous sets implies (in ZF) the existence of infinite opc lattices.
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。
