(参考) https://en.wikipedia.org/wiki/Axiom_of_regularity Axiom of regularity However, regularity makes some properties of ordinals easier to prove; and it not only allows induction to be done on well-ordered sets but also on proper classes that are well-founded relational structures such as the lexicographical ordering on {(n,α )| n∈ ω ∧ α is an ordinal } Given the other axioms of Zermelo?Fraenkel set theory, the axiom of regularity is equivalent to the axiom of induction. The axiom of induction tends to be used in place of the axiom of regularity in intuitionistic theories (ones that do not accept the law of the excluded middle), where the two axioms are not equivalent. (引用終り) 以上
