[過去ﾛｸﾞ] 純粋・応用数学（含むガロア理論）8 (942ﾚｽ)
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660: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2021/05/30(日)13:38 ID:kTzpB/An(11/15) AAS
>>659
つづき

https://en.wikipedia.org/wiki/Epsilon-induction
Epsilon-induction
In mathematics, ∈-induction (epsilon-induction or set-induction) is a variant of transfinite induction.
Considered as an alternative set theory axiom schema, it is called the Axiom (schema) of (set) induction.
It can be used in set theory to prove that all sets satisfy a given property P(x). This is a special case of well-founded induction.

Contents
1 Statement
1.1 Comparison with natural number induction
2 Independence

ndependence
In the context of the constructive set theory CZF, adopting the Axiom of regularity would imply the law of excluded middle and also set-induction. But then the resulting theory would be standard ZF. However, conversely, the set-induction implies neither of the two. In other words, with a constructive logic framework, set-induction as stated above is strictly weaker than regularity.
(引用終り)
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