21/10/25 07:50:36.59 wB/2IR+g.net
>>553
つづき
Two model-theoretic characterisations of inaccessibility
Firstly, a cardinal κ is inaccessible if and only if κ has the following reflection property: for all subsets U ⊂ Vκ, there exists α < κ such that (V_α,∈ ,U∪ V_α) is an elementary substructure of (V_{κ },∈ ,U). (In fact, the set of such α is closed unbounded in κ.) Equivalently, κ is Π _{n}^{0}-indescribable for all n ≧ 0.
It is provable in ZF that ∞ satisfies a somewhat weaker reflection property, where the substructure (V