>>402
>Vκ（κは最小の到達不能基数）は
>到達不能基数の存在公理のない集合論Aのモデルになりえるが
>（その場合Vκ＝Vなので集合ではなく固有クラス）
>到達不能基数の存在公理のある集合論Bにモデルにはなりえない
>（そしてそのような集合論Bの中では集合として存在することが証明できる）

何をいわんとしているか 意味不明
下記を百回音読してね

(参考)
https://en.wikipedia.org/wiki/Inaccessible_cardinal
Inaccessible cardinal
In particular, inaccessible cardinals need not exist at all. That is, it is believed that there are models of Zermelo-Fraenkel set theory, even with the axiom of choice (ZFC), for which no inaccessible cardinals exist[2]. On the other hand, it also believed that there are models of ZFC for which even strongly inaccessible cardinals do exist. That ZFC can accommodate these large sets, but does not necessitate them, provides an introduction to the large cardinal axioms. See also Models and consistency.

The existence of a strongly inaccessible cardinal is equivalent to the existence of a Grothendieck universe.
If κ is a strongly inaccessible cardinal then the von Neumann stage Vκ is a Grothendieck universe.
Conversely, if U is a Grothendieck universe then there is a strongly inaccessible cardinal κ such that Vκ=U.
As expected from their correspondence with strongly inaccessible cardinals, Grothendieck universes are very well-closed under set-theoretic operations.

https://en.wikipedia.org/wiki/Large_cardinal
Large cardinal
The proposition that such cardinals exist cannot be proved in the most common axiomatization of set theory, namely ZFC, and such propositions can be viewed as ways of measuring how "much", beyond ZFC, one needs to assume to be able to prove certain desired results.
In other words, they can be seen, in Dana Scott's phrase, as quantifying the fact "that if you want more you have to assume more".[1]