>>640 追加
・『巨大基数はフォン・ノイマン宇宙 V の文脈で理解される。これは冪集合を取る操作を超限回反復して得られるもので、与えられた集合の全ての部分集合を集めたものである。典型的には、巨大基数公理が成り立たないようなモデルは、巨大基数公理が成り立つような何らかのモデルの自然な部分モデルになっている。例えば、もし到達不能基数が存在するなら、そのような基数が現れる最初の高さで「宇宙を切り離して」しまうと、到達不能基数が存在しないような宇宙が得られる』
　つまり グロタンディーク宇宙Uは 到達不能基数が存在する宇宙であり
　到達不能基数が存在しないようなフォン・ノイマン宇宙 V は、グロタンディーク宇宙Uより小さい
・『また、もし可測基数が存在するなら、冪集合操作を「定義可能な」程度に反復するよう抑えると、ゲーデルの構成可能宇宙 L が得られ、そこでは「可測基数が存在する」という主張は成立しなくなる (even though it contains the measurable cardinal as an ordinal)』
　で 可測基数 下記 Measurable cardinalを百回音読してね（＾＾
　つまり、ゲーデルの構成可能宇宙 L 内には 巨大基数は存在しえない

(参考)
https://en.wikipedia.org/wiki/Large_cardinal
Large cardinal
(抜粋)
Motivations and epistemic status
Large cardinals are understood in the context of the von Neumann universe V, which is built up by transfinitely iterating the powerset operation, which collects together all subsets of a given set. Typically, models in which large cardinal axioms fail can be seen in some natural way as submodels of those in which the axioms hold. For example, if there is an inaccessible cardinal, then "cutting the universe off" at the height of the first such cardinal yields a universe in which there is no inaccessible cardinal. Or if there is a measurable cardinal, then iterating the definable powerset operation rather than the full one yields Gödel's constructible universe, L, which does not satisfy the statement "there is a measurable cardinal" (even though it contains the measurable cardinal as an ordinal).

https://en.wikipedia.org/wiki/Measurable_cardinal
Measurable cardinal
In mathematics, specifically in set theory, a measurable cardinal is a certain kind of large cardinal number. In order to define the concept, one introduces a two-valued measure on a cardinal
κ, or more generally on any set. For a cardinal
κ, it can be described as a subdivision of all of its subsets into large and small sets such that
κ itself is large, the empty set and all singletons
{α} with
α∈κ are small, complements of small sets are large and vice versa. The intersection of fewer than
κ large sets is again large.[1]
It turns out that uncountable cardinals endowed with a two-valued measure are large cardinals whose existence cannot be proved from ZFC.[2]
The concept of a measurable cardinal was introduced by Stanisław Ulam in 1930.[3]