19/03/10 11:06:23.72 rk/29Zdt.net
>>143
＜Well-founded relation（後述引用ご参照）＞
１）
”on a class X if every non-empty subset S ⊆ X has a minimal element with respect to R, that is an element m not related by sRm (for instance, "s is not smaller than m") for any s ∈ S. In other words, a relation is well founded if
(∀ S ⊆ X)[S ≠ Φ → (∃ m ∈ S)(∀ s ∈ S) ￢ (sRm)].”
（>>138）「(Set9) 正則性公理 ∀a[a≠Φ→∃b(b∈a∧a∩b=Φ)]」などと対比するのが、分り易いかも
つまり、正則性公理は、set theoryだが、on a class Xとして、”Well-founded relation”を一度理解して、
それとの比較で、正則性公理を考える（∈を使った順序の中の話しとして、考えるべしと）
２）
”In set theory, a set x is called a well-founded set if the set membership relation is well-founded on the transitive closure of x.
The axiom of regularity, which is one of the axioms of Zermelo?Fraenkel set theory, asserts that all sets are well-founded.”
正則性公理の説明
３）
”When the well-founded relation is set membership on the universal class, the technique is known as ∈-induction.”
”∈-induction”というのは、集合論で最初に使う”∈を使った順序”での、induction（帰納法）だよと
つづく