广义控制数的一个下界
A Lower Bound for Generalized Dominating Numbers
摘要：
证明了当$κ$和$λ$是满足$λ^ κ= λ$的无穷基数时，从$λ$到$κ$的处处控制序函数集的共尾性是$2^λ$ .一个较早的证明是一个结果的独立家庭的职能。新的证明直接遵循我们提出的主要定理：对于每个$A \subseteq λ$有一个函数$f: {^κλ} \to κ$，使得只要$M$是$\textrm{ZF}$的传递模型，使得${^κλ} \subseteq M$和$M$中的某些$g: {^κλ} \to κ$支配$f$，则$A \in M$。也就是说，“可建构性可以被简化为支配性”。
英文摘要：
We show a new proof for the fact that when $κ$ and $λ$ are infinite cardinals satisfying $λ^ κ= λ$, the cofinality of the set of all functions from $λ$ to $κ$ ordered by everywhere domination is $2^λ$. An earlier proof was a consequence of a result about independent families of functions. The new proof follows directly from the main theorem we present: for every $A \subseteq λ$ there is a function $f: {^κλ} \to κ$ such that whenever $M$ is a transitive model of $\textrm{ZF}$ such that ${^κλ} \subseteq M$ and some $g: {^κλ} \to κ$ in $M$ dominates $f$, then $A \in M$. That is, "constructibility can be reduced to domination".
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。
