15/12/30 21:30:40.13 mXaeJ8Mj.net
>>527
>同終性、共終性の概念かー、知らんね（＾＾；
共終性は下記（Cofinality）か。同終性は、検索ヒットしないから、共終性と同義で使われなくなったということか？皆さん物知りだね～（＾＾；
URLﾘﾝｸ(ja.wikipedia.org)
連続体仮説
他の多くのアレフ数に対しても同様のことが言えるが、一部のアレフ数については共終性に基づくケーニヒの定理によって除外される
ケーニヒの定理 (集合論) 2.2 ケーニヒの定理と共終数 URLﾘﾝｸ(ja.wikipedia.org)
共終数 URLﾘﾝｸ(ja.wikipedia.org)
URLﾘﾝｸ(en.wikipedia.org)
The continuum hypothesis
The same is true for most other alephs, although in some cases equality can be ruled out by Konig's theorem on the grounds of cofinality,・・・
URLﾘﾝｸ(en.wikipedia.org)
In mathematics, especially in order theory, the cofinality cf(A) of a partially ordered set A is the least of the cardinalities of the cofinal subsets of A.
This definition of cofinality relies on the axiom of choice, as it uses the fact that every non-empty set of cardinal numbers has a least member.
The cofinality of a partially ordered set A can alternatively be defined as the least ordinal x such that there is a function from x to A with cofinal image.
This second definition makes sense without the axiom of choice. If the axiom of choice is assumed, as will be the case in the rest of this article, then the two definitions are equivalent.
Cofinality can be similarly defined for a directed set and is used to generalize the notion of a subsequence in a net.